This is right. But to put it much more generally, and as an exercise in seriously trying to bridge information gaps:
To buy stocks you need what is called a Brokerage account. The way a brokerage account works is that you give money to the Broker to invest for you. (Generally, you will do this by transferring it from an existing bank account.) This money generally gets put into a highly liquid account in your name, such as a money market fund. You can get your money back by instructing your broker to send it back to you.
When you want to buy stocks or other financial investments, you direct your broker to use the money in your brokerage account to buy stocks or other financial investments in your name. Your broker will use the money that is in your account to do this. Your brokerage account now also contains the stock you bought.
When you want to sell stocks, you tell your broker to sell, and the proceeds get put back into your cash-like account.
Brokers make money by charging you a fee each time you buy or sell a stock or other financial investment through them.
There are full-service brokerages and discount brokerages. Full service brokers (such as Merrill Lynch) give you extra help figuring out what you want to do, though they charge a premium. Be aware that since full service brokers do not have a fiduciary duty to their customers to give good advice, they can legally steer you toward investments that pay them a higher commission even if it's not as good for you.
Discount brokerages are usually online-only and charge lower commissions. You don't get any advice, just the ability to buy and sell through their website. E*trade, Scottrade, and Zecco are well-known discount brokers. Some major banks such as Bank of America / Merrill Lynch and Fidelity also offer online brokerage services, as does Vanguard. Many people recommend discount brokerages over full-service ones.
I've had good experience with ShareBuilder.
I am beginning to suspect that it is surprisingly common for intelligent, competent adults to somehow make it through the world for a few decades while missing some ordinary skill, like mailing a physical letter, folding a fitted sheet, depositing a check, or reading a bus schedule. Since these tasks are often presented atomically - or, worse, embedded implicitly into other instructions - and it is often possible to get around the need for them, this ignorance is not self-correcting. One can Google "how to deposit a check" and similar phrases, but the sorts of instructions that crop up are often misleading, rely on entangled and potentially similarly-deficient knowledge to be understandable, or are not so much instructions as they are tips and tricks and warnings for people who already know the basic procedure. Asking other people is more effective because they can respond to requests for clarification (and physically pointing at stuff is useful too), but embarrassing, since lacking these skills as an adult is stigmatized. (They are rarely even considered skills by people who have had them for a while.)
This seems like a bad situation. And - if I am correct and gaps like these are common - then it is something of a collective action problem to handle gap-filling without undue social drama. Supposedly, we're good at collective action problems, us rationalists, right? So I propose a thread for the purpose here, with the stipulation that all replies to gap announcements are to be constructive attempts at conveying the relevant procedural knowledge. No asking "how did you manage to be X years old without knowing that?" - if the gap-haver wishes to volunteer the information, that is fine, but asking is to be considered poor form.
(And yes, I have one. It's this: how in the world do people go about the supposedly atomic action of investing in the stock market? Here I am, sitting at my computer, and suppose I want a share of Apple - there isn't a button that says "Buy Our Stock" on their website. There goes my one idea. Where do I go and what do I do there?)