Anyone can invest on stocks and there is no any restrictions to buy stocks for F-1. I would suggest to call brokers like ameritrade, merril edge and many more others. They will help you to open a brokerage account. Before buying stocks, it is very important to do a good research on companies where you are investing. You should know how the company is growing, profit and market capacity. Do not spend all in one stock, it is better to put money on different stocks. Also, you wouldn't not expect it to grow  in a day or a month or a year. You got  a have guts and patience. Here is my suggestion for 2013 and I personally prefer dividend stocks.

1.AUY/GG (gold stocks: low price and it won't stay like this forever)
2.EGAS/LINE(natural gas stocks: good dividend and high chance of growing)
3.INTC/CSCO (technology: slow growth but worthy)
4.BAC/HBAN (Banking: hurt by economy in the past but good indication of growing)
5. T (telicommunication: also good dividend)


P.S: you buy stocks when the price is low and sell it whe it is high.