Magic may definitely seem intimidating. It's got a rulebook over 200 pages long, and passed 10,000 unique cards back in 2008. I'm sure you've heard stories of people spending tons of money on magic collections. But, done right, Magic can be quite approachable and quite affordable. Whether or not this is "easy" depends on your goals. If you just want to play magic with friends and have fun, then this can be done quite easily. If you want to win tournaments, this will take a lot work. There is a whole spectrum in between.

Learning to Play

If you have a friend or friends who play Magic, odds are they will be very happy to induct you into the cult teach you how to play. Having friends who already play or want to learn with you is also really important because having a dedicated play group will make learning a much more pleasant process. If you don't have such a group, see if your local game store has casual events so that you can find one. Learning to play against strangers is a much less forgiving experience.

There are potentially a surprising number of people in your life who already do or once have played Magic (especially if you already have friends that play other CCGs). Try leaving a few decks of Magic cards on your desk and see how many people go, "Oh, you play Magic too?"

If you don't have friends who already know how to play, you can read the Magic basic rules, which are only 18 pages. These describe the bulk of the mechanics you need to understand to play (although somewhat comically omits the most important 2 pieces of information: you start with 20 life and lose when you hit 0).

Duels of the Planeswalkers is also a decent tutorial in computer game form if you prefer that medium, although it can get a bit slow due to the game waiting to see if you want to do something every time you could do something (which is quite often in Magic). Magic: The Gathering Arena is another digital option for leaning to play.

My personal belief is that Magic is best played in-person. It wasn't designed or optimized to be a digital experience. A digital version of Magic can be a good way to learn and can let you play when your playgroup is not around, but if you have physical decks and a playgroup that you can get together, you should do so.

The Card Pool

While the card pool seems the most intimidating aspect of the game, it's a bit of a red herring. When playing a game, you only care about the cards you and your opponent are using. A normal deck is 60 cards. Typically over a third of a deck is going to be lands, which don't vary that much. That means that in a normal game of magic (i.e. not Commander), there are fewer than 100 distinct cards you need to think about, which is less than 1% of the card pool.

Even when you start building your own deck, you will be limited to your collection which, at first, will probably be much smaller than 10,000 cards, and probably under 1,000 distinct cards. Only when you want to expand your collection or build a competitive deck do you start to care about all cards in Magic, but even then, not necessarily. If you want to expand your collection, start with a search tool (such as scryfall.com) and look for cards you want, or a site where people post decklists that you can use as a starting point to look for particularly exciting cards. Meanwhile, if you want to get into the tournament scene, you can (and should) start with a tournament format with a limited card pool or one that doesn't require you to have a massive collection; more on that later.

Building a Collection

If you have a group of friends that already know how to play, odds are one of them will have decks that you can borrow when you are starting. Just make sure to tell them you want to borrow an aggro deck, as using a combo or control deck is terrible when learning to play (If no one in your playgroup has any aggro decks on-hand, try finding a different play group :P).

Alternatively, if you have a group of friends that are learning Magic together, consider either making some bulk purchases together that you will split among the group, or having one person buy cards that everyone will use at first (until people have built out individual collections).

If you want to start playing without needing to build a collection, buy some preconstructed decks. Wizards prints these pretty frequently, and they can give you a great starting point in terms of having a deck that works, so you can start playing right away, then step up to tweaking the deck, and then eventually try to build one from scratch. Check out the Ravnica Guild Kits as a good example. These are especially good if you have a group of players all learning Magic together.

If the deck building is what excites you most about magic, you should get a Deck Builders Toolkit (from any recent set) and/or look online for someone selling a bunch of cards for cheap. You can often get a bunch of cards in bulk for around 1-2 cents a card on the secondary market; these aren't going to be the best cards or tournament staples, but they will be a bunch of cards that you can start building decks with.

Building a Deck

Building a deck is a skill unto itself. There is a lot of advice on how to actually do it. I'm not going to try to tackle that here. This is just a few pieces of advice on how to approach deck building (rather than on how to do it).

If you have friends who are established players, ask them what they take into consideration when building a deck. Tell them what you want a deck to do (after you've played a few games) and have them help you build it. Otherwise, start with a preconstructed deck.

Once you have your own deck, play it and tweak it after every few games. Take out cards you don't like, or cards that keep feeling weak, or cards you keep not being able to afford (mana-wise). Put in cards that are exciting, or cards that do things you keep being frustrated at not being able to do, or cards that have a better mana cost, or cards your opponents used to trounce you.

Once you've tweaked a deck for a while, make another one. Then tweak that one. Do this enough times and you'll get a sense for how to build a deck. And, better yet, you'll get a sense for how to build the type of deck you like to play.

Beginner-Friendly Formats

The most beginner friendly "format" (and the one I use when teaching people how to play Magic) is regular 1-on-1 60-card Magic, but where your deck (you being the beginner) is much better than your opponent's deck. This gives you plenty of room to make mistakes and still possibly come out on top. If you have a friend who is both an experienced player and a good sport, go for this.

Alternatively, if no one in your playgroup knows how to play very well, this is usually sufficient beginner-friendliness that format doesn't matter. No one has vast expertise to throw around. Just make sure no one has spent wildly more money buying cards and this should shake out pretty well.

If you are joining an experienced playgroup with competitive people, try for multiplayer (either free-for-all or something exciting like Star Power). My first ever game of Magic was against two very experienced friends, yet I still won because they spent the whole game fighting each other (because I had no idea what I was doing), and then I was able to finish them both off. Two-headed giant is also a great format possibility as you have an ally that can give you unbiased tactical advice and help you with rules questions without giving away too much information to your opponents.

I'd stay away from Commander at first. It is a very fun format, is multiplayer, and is often more about doing interesting things than it is about winning. I highly recommend it... once you know what you're doing. However, as a new player, there are a lot of pitfalls: there are a lot more cards you will have to care about in a commander game (due to the restriction that you have only one of each card in a deck), the complexity of the game state tends to get much higher than that of a normal magic game, and Commander games tend to run much longer than normal games, making mistakes more expensive.

Tournaments

Tournaments are a totally optional part of Magic. I have friends who have played Magic for years and never played in a tournament. But they are also an option if that's what excites you.

Magic has 3 general types of tournaments: Sealed, Constructed, and Draft. Sealed is a tournament where you open a set of cards at the tournament, build a deck out of them (plus basic lands), and then play with that deck. Draft is similar, except that it has a complex process for how you select the cards you keep. Constructed is where you bring a deck you have made and play against other people who have done the same.

If you are a new player who wants to get into tournaments, I recommend sealed tournaments. These are much more affordable price-wise (all it costs is the admission price; you don't have to spend hundreds or thousands of dollars on a deck), you often get to keep the cards you open (thus growing your collection), and the games themselves tend to be a little more straight forward (it's more about cards that stand on their own merit rather than complex card interactions or decks tuned to the metagame).

While all of these things describe both sealed and draft, draft adds the added complexity of the card selection process, which is yet another skill to learn (worth doing eventually, but not needed at first). In sealed, it's just rudimentary deck building and playing magic. Set releases or prereleases are especially good for new players because at that point, people haven't had as much chance to use the cards in that set, thus reducing the experience bias even more.

If you want to get into constructed, there are a bunch of formats within that genre (Standard, Modern, Legacy, and Vintage being the big 4). You should probably start with Standard, in which only cards from the most recent few sets are legal, thus reducing the number of cards you will need to learn to be competitive in the tournament format.

I'd recommend playing for at least a few months before joining a tournament. You need to be at least moderately proficient in the rules before you play in one (regardless of format) because your opponent will almost never let you take back a mistake in tournament play. Additionally, you need to either have some practice in deck building (especially for sealed or draft) or have copied a competitive decklist (if you're playing constructed and don't want to design your own tournament-grade deck).

Magic the Gathering is actually one of the easiest TCG to get in.

It has entry products aimed at beginners or people trying to get in mainly :

• 
  Construction Kits
  
  Give a lot of lands (you need them for basically anything) and
  quite a lot of cards of each color and some of each dual color. The
  power level isn't especially high, but it also contain boosters. All
  in all, a very fine way to start a collection. There's a leaflet in
  the kit with advice on "How to build a balanced deck ?" which will help you to
  tinker with the deck on your own.


• 
  

  Planeswalker decks
  
  Give you access to every card
  types (or so) there is in magic, you've got some unique cards and
  staple commons/uncommons. The decks' plans are usually quite
  straightforward and made with playability in mind, they aren't
  competitive, but they surely can be played as in.

  
  
  

  _{N.B. Premade decks in previous times were either stupidly powerful or
  contained especially potent cards (e.g. Rats deck of Kamigawa, Elf deck
  of Lorwyn etc) or gimmicky at best (all the other Kamigawa decks
  etc). The cards in it weren't especially useful outside of the deck's
  theme, so it was kinda hard to learn Magic with them. Nowadays you've
  got planeswalker decks.}

  
  


• 
  Challenger decks
  
  Tournement ready decks. These products usually are quite competitive and allow one to see the meta and explain how the deck works, usually they are quite instructive.


• 
  Game Night
  
  Contain 5 decks made on a theme based on the color (graveyard is actually
  useful + zombies for black etc). These decks aren't
  especially powerful but are made for beginners to "feel" what each
  color is about, as well as get a taste for multiplayer. I found it quite instructive.

The main difference between Magic and Yu-Gi-Oh is the resource management, you can play as many monsters as you want every turn, but you need to pay the cost. Which depends on the land cards. All in all, the Magic rules are quite simple,
but card interaction isn't. You'll understand quite all of it very quickly by playing.

MTGArena (the latest video game version of Magic) is also a very good way to learn the rules, and get a feel for how phases work and how the game plays out. The theme decks that are given in the beginning are not very strong though, and some of them are barely playable as is. MTG Arena is a Free-to-play version of Magic so it is the easiest version to try things out in.

Magic is designed to be easy to get into and hard to master. On one level, casting creatures and throwing them at the opponent is very easy to do. On the other, interacting with the stack, timing your ability activations, spells and land drops, and mastering sideboarding/mulligans is very difficult. It's easy to play Magic and even as a complete beginner you'll beat good players some of the time; however to play Magic perfectly in a 15-round tournament is pretty much humanly impossible.

Here're three articles from ChannelFireball written by a Magic Hall of Famer on how difficult Magic's decks are. Even if you don't know the rules, you should be able to get the gist: there are decks in which you make simple and/or the same decisions every game, and there are decks which give you a ton of options. Naturally the more options you have, the more likely you are to make a mistake, but also to outplay your opponent.

In terms of expense, if you want to play on paper, Magic can be quite expensive. Many of the more powerful rare cards & mythic rare cards can cost US$ 10+. However if you're okay with playing online only, then Magic Arena is free to download, and if you grind enough you can eventually unlock all the cards.

While the other answers cover structure and resources of the game, I think the most useful answer is to draw some light on the ways of actually getting to learn the game, and evaluate from there.

Either way, learning the game will be a process, not something you'll do in a day like you'd expect from a board game with a four-page manual. Instead, you'll be learning more and more of the mechanics, while the people around you will likely correct more and more of your mistakes, all while already playing the game. Even when you're reasonably experienced, new editions will introduce new mechanics, so you'll keep picking up things as you go.

I actually don't think MtG is a game that's easy to learn, as its ruleset is overwhelming to even experienced players sometimes. There also aren't just the rules, but the language to learn that players will use at the table. That said, the complexity makes it interesting, and you can approach learning it a few different ways.

Being taught by a friend

Almost everyone I ever met playing MtG has been taught by a friend, and many of these friendships have established in local game stores. While the possibilities are different today especially over the internet, I still meet a lot of beginner players in the store, so I think it's worth being mentioned.

However you come by someone to teach you, if you know someone who already knows the rules reasonably well, I would say that's the best way to pick up the game. Having someone to answer your specific questions prevents many of the barriers you might encounter trying to read the rules.

And of course by playing with a friend, you'll already have fun while learning!

Learning by watching or attending local events

I have organized and judged FNM and prerelease/release tournament events at a local store and local conventions for a few years now, both being formats that are supposed to be welcoming and tailored towards new players. At tournaments, you are expected to know a little bit about the game, while FNM events the way I know them are gatherings without specific expectations and therefore without prerequisites.

I will say that no matter how beginner-friendly you're trying to make those events, it's tough picking up the game from simply being around experienced players. The more you're used to the game, the quicker you go through the motions, making it very hard to follow unless you already know what's going on. Additionally, you're more likely to feel discouraged to ask questions because you're pausing multiple people's games, or even prolonging an ongoing tournament.

Nevertheless, if you don't know anyone playing the game yet, I suggest that you visit local events just to meet people. You might even ask if someone would spend the time to explain the basics to you - there's probably someone around willing to teach, and people are generally happy to expand their player group in my experience.

I want to point out that some of those events will be so-called Sealed events, meaning everyone gets a number of boosters to build their decks from. As soon as you picked up the basics, this equalizes the playing field in terms of investment at least, as you won't have to compete against decks worth hundreds or thousands of dollars with your starter kit cards. As mentioned in the comments, there are other ways in which a store in general can help you get started as well.

Learning by playing digital versions of the game

I looked into both Duels of the Planeswalkers and Magic Arena, and the fact that they take care of most of the rules makes getting started with the game relatively easy. Understanding some mechanics like how to attack, or win/lose conditions are well conveyed, while others such as paying costs and when to tap and not to tap will generally be less apparent. Still, you might be able to pick up how the game works enough to play a couple of "actual" games.

Although I find this method to be the least favorable, I wouldn't call it a bad alternative. You will learn the game, and if you can't find a local store and don't know anyone else playing it, it's still a good option. Nevertheless, when I observed players on MtG Arena, I could tell that they are generally making choices an experienced player would catch right away. If you would be sitting at the same table as that player and made that mistake, chances are they would let you know and help you learn that way. While I don't have any data backing it, I would imagine that learning process is a lot more tedious playing a digital version of the game.

Learning from videos or other guides

I think this method of learning is mostly useful for picking up advanced mechanics or interactions, not as much for starting to learn. Beginner videos will be joyfully explaining what tapping and paying costs is, but due to the lack of interaction, you should quickly find yourself in a situation they didn't cover, and be left wondering what to do. Also, wanting to learn the game probably means you want to play either at a physical or digital table in the long run, so in my opinion, just skip the guides and go there straight away.

However, if you are completely new to the concept of trading card games, they might be interesting in order for your to evaluate what you're getting yourselves into.

I learned to play in 10 minutes with some friends, I've taught plenty of people to play in the same time frame. The basic rules of "play a land, cast a spell" are really straightforward.

There is a lot of hidden depth and complexity when you get into it but you don't need to know all that to start playing. I've even answered rules queries at the top tables of a competitive tournament where people lacked basic knowledge of the stack and yet had still made it that far.

Your best bet is to find a friendly local store and go along and play or to try playing in Mtg:Arena online.

Try and find a sealed event (there is a pre-release coming up soon) or a draft as then you do not need to bring your own deck. Instead you open cards and then play using those cards. Drafts are trickier than sealed as you need to know how to draft but again a quick intro will give you enough to get started and then you can learn from there.

Just expect to lose a bit while you learn :)