Open an account with either an online brokerage or a penny stock firm. If you are not familiar with trading penny stocks, try starting with a penny stock broker. There are also a great many newsletters and sources of research that provide recommendations on penny stocks.
Trade penny stocks with paper money until you feel that you're ready to trade with real money. There are many programs that will allow you to do this; take your time until you get a feel for the penny stock market and how it interacts with the larger markets.
Invest a small amount to begin with. If you can make this amount grow, then you can add to your principal. But protect yourself by limiting your initial investment so that you don't lose your shirt. Don't keep pumping additional principal into your account if you lose at first; this is a recipe for disaster.
Stick closely to your trading program or analyst recommendations and don't let emotions start dictating your actions. You will need to keep your fear and greed in check in order to succeed at penny stock trading. Most investors are controlled by greed and fear, but speculators who make money can get past these emotions when they make trading decisions.
Use the profits you make from trading penny stocks to reinvest into the program. This is perhaps the safest way to grow your profits over time. If you clean up on one stock, use the gain to purchase others. This provides you with additional diversification without requiring additional principal.