here is what I did, and have been very successful doing it. Don't read anything until you have read the following:
One Up On Wall Street, by Peter Lynch
The Intelligent Investor, by Benjamin Graham
The first one is written in plain English and primes you for the only way to successfully invest in stocks: find great companies that are undervalued, and invest for the long term. If you never read another book about investing, read this one. The second nearly takes an advanced degree in statistical financial analysis to decipher, but if you can slug through it and catch the basic points, it will take you to the next level. This is the Bible that Warren Buffett preaches from (Buffett was a student of Graham's).
As for websites, eTrade, ScottTrade, and TD Ameritrade all provide low-cost trading and incredibly good research on stocks and mutual funds.
Finally, I'd suggest reading at least the first book and then setting up a dummy account on any number of websites. You can start with an imaginary balance, "buy" stocks, hold them, and see how your selections do over time. I did this at MSN Money back in the day. If you are good at finding good stocks, proceed with real money. If you are not, hone your skills or buy 5-star mutual funds and let the experts do it.
I started with $1,000, turned it into $3,000 in six months, then put $10,000 in and turned it into $25,000 in 24 months, all while I was in college. It gave me a great start coming out of school. This was 2003-2005, so I was helped by good timing, but now is a phenomenal time to buy, in my opinion.