Go to
Ameritrade or
Datek or similar, and make a new IRA account. The initial deposit has to be at least $500, if I recall correctly.
You have an important choice to make when you start the IRA. Roth or Traditional.
Traditional means that you can deduct from your income the first $2000 you place in the account (I think). So if you made $28k in 2001, but you deposited $2000 (or more) into a traditional IRA, you could effectively report that you made $26k and pay less taxes RIGHT NOW. When you are 62 and take money out of that account, you pay taxes on it THEN.
Roth IRA (my preference) work the other way around. You just put money in them (probably subject to some limit or other, can't remember) and pay taxes on all your income, including the part you stuck in the IRA RIGHT NOW. But when you take that money out of the account at age 62, it is tax free THEN.
Once the account is funded with your money, you're free to buy mutual funds, stocks, bonds, precious metals, and whatever else is traded by the broker you selected for your account. The fundamental idea for investing is to "buy low, sell high". You can take more risks when you're younger, and should take fewer as you approach retirement.
If you want specific stock advice, try
The Motley Fool which seems to be advocates of the get rich slowly philosophy. If you want my advice, buy gold mining stocks RIGHT freaking now because gold prices must rise due to the incredible shortage of physical gold in the market. It may not happen right this second, but it's inevitable.
edit: OTOH, it looks like maybe you were asking whether or not you should make an Individual Retirement Account or simply a brokerage account (i.e. cash account). It would be silly to start investing in a cash account, by which I mean a simple brokerage account in which you try to make a profit, without first setting up an IRA. Get an IRA and a 401k (company retirement account) going as soon as you can afford to. In a 401k, you put in a percent of your paycheck, and the company you work for matches your contribution. Your contribution is doubled from the start(!)
After you have your retirement accounts initiated, and after you've paid off all your credit cards, you can then see if you have enough disposable income for a cash account.