Step 1) Read about it via primers on websites such as "The Motley Fool" (Fool.com) + Investopedia.
Step 2) Read books about it to expand on the website stuff
Step 3) Play fantasy stockmarket web games based on real data to get your head round putting into practice what you've learned so far, without risking any real money, including (but not limited to) the Caps game on the Motley Fool.....
Step 4) Get a stock trading account from a reputable financial institution, such as Sharebuilder.com (now part of CapitalOne, last time I looked 'em up) to get actually trading with real money when you feel ready.... if you go in unprepared, you'll get your ass handed to you on a plate.
More places to find advice on this sort of stuff can be found by clicking here to see what personal finance websites are available on the interweb.