You need to open an account with a brokerage firm. Both Ameritrade and E*Trade are good and have pretty cheap trades (about $10 per trade). Compare to $20~$50 per trade at some of the larger full-service brokers.
If you want to invest and trade in stocks you really should educate yourself before using real money. I really like The Motley Fool as a place to learn about stocks and trading.
If you're still interested in finding out more, I suggest you pick up a book (or three) by the Motley Fool guys. Go to Amazon and type in Motley Fool and you'll find several that are great, such as The Motley Fool You Have More Than You Think : The Foolish Guide To Personal Finance, The Motley Fool Investment Guide : How The Fool Beats Wall Streets Wise Men And How You Can Too and The Motley Fools Rule Breakers Rule Makers : The Foolish Guide To Picking Stocks. Or better yet, check out their website at www.fool.com -- they're a couple of guys who used to work on Wall Street, but decided to educate the vast public. Another great link (who will give you more advice along the lines of the first paragraph) is www.daveramsey.com -- He's got great money advice and a radio show you can listen to online or call in with questions, etc.
Hope this helps....