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You can open a brokerage account with any of the popular discount brokers: Schwab, Fidelity, Vanguard, etc. Just go to their web sites and follow the steps to open an account. If you need a bit more hand-holding, which is normal for new investors, you can drop into one of their offices and they're happy to help. Fees are generally low all around (~$5 per trade), so you can't go wrong with a name-brand discount broker. The middleman is cheap!

The easiest way is to open an account with a major broker, and place a market buy order. The commission for most of them is $5-10 per trade, which IMO is basically negligible if you are actually planning to buy a significant quantity and hold it long-term. Robinhood has no commission, but I would recommend you use a more established broker - Robinhood is pretty new, the interface isn't the best, and I wouldn't consider it something that you can just forget about for many years.

Cutting out the middleman here is not a practical idea. The middleman is actually helping you a lot. Trading on the market is complicated and a lot of work, the broker is doing all the hard work of finding sellers and complying with the regulations for you. The cut they take is very small unless you are making many trades, and they are unlikely to cheat you because of very strict government regulations. There are also some nice benefits to having a broker, like FDIC insurance.

It might also be worth looking into the actual companies themselves, some allow you to invest directly through them and you can even have it so that they will reinvest dividends (if they have them) for you.

ETrade or Fidelity should let you do what you do easily. They have very modest trading fees, and those fees are it. No hidden charges.

Remember holding a stock longer than 1 year means the capital gains will be taxed at a much more favorable rate.

If you don't want to be actively involved in investing, you ought to at least read John Bogle's book "Common Sense on Mutual Funds". That debunks a lot of the "artificial complexity" of stocks.

Another interesting thing worth studying is how your local university invests their Endowment. They are required by law to invest it for maximum growth, and their tactics are surprisingly standardized.

Open an account at a brokerage firm. I use Fidelity but others recommended above are good too. You can also open an IRA through these brokerage firms and invest from your IRA.

Buying individual stocks does require some homework to make the good choices. If you don't want to spend time doing homework put your money in an index fund. Investing time developing your career is a better investment than investing time picking stocks, especially if you are only working with a few thousand dollars.

If you plan to invest in one go (which is generally not recommended, especially if you don't know exactly what you are doing and if you want to hold it for a longer time, this is called market timing) then the fees are pretty small compared to the amount of money you want to invest. Usually, it is recommended to buy it over a few days, weeks, months, to minimize the risk a little bit. Thus, you are less susceptible to the volatility of the stocks.

Usually you have to pay a one-time fee independent of how many stocks you buy. So if you buy your stocks with multiple purchases, the fees might start to matter for you.

If you don't want to look at it at all I would recommend one of the more mature platforms and just pay the fees (I use AllyInvest or ETrade).

If you care about those fees, you might want to use a platform that doesn't charge you any fees (I use Robinhood, but you might need to watch the platform now and then and see what changes they implement, since they are really you and keep changing stuff). I am sure there are a few others with free trades as well.

That is just my personal experience/opinion.