Bet that a stock will rise by purchasing a call option. If you own a call option, you have the right to purchase the underlying asset at the strike price. You don't have to exercise this right unless it is profitable. For example, say you buy a call option for stock S, currently trading at $10 per share, with a strike price of $12 at a premium of $0.10 for a total cost of $10. If company S remains below $12 you won't exercise your option, but if it goes above $12 you will. Your profit, if you sell the shares right away, is the total value of the shares above $12 minus the $10 you paid for the contract.
Make money on a stock you think will fall with a put option. A put is almost the opposite of a call. Instead of buying a contract that guarantees a purchase price, you buy one with a fixed sale price for the underlying asset. In another example with stock S, if you buy a put with a strike price of $9 when S is trading at $10, you profit if the stock goes down below $9 per share because you can buy the shares for less than $9 but still sell them at that price.
Profit from selling options. A slightly more advanced, and risky, strategy is selling options. When you sell an option, you must have a margin, either reserve funds or a line of credit, to cover the potential cost. If you buy an option your risk is limited to the cost of the option. When you sell an option you get the premium immediately, but if the option is exercised your risk is either unlimited (for a call) or high (if you sell a put, the worst that can happen is the stock falls to zero).
Trade options to hedge your stock investments. If you own stock you can buy or sell options to limit your risk exposure. For example, say you own stock S, currently trading at $10. If you are afraid stock S will go down over the short term. Rather than sell the stock and incur brokerage fees, you can sell a call. If the stock price does decrease, you profit from the sale price of the option. If it increases your risk is minimized by the stock you hold.
Experiment with options with other assets. Options are traded for assets other than stocks, including stock market indexes, real estate, futures and bonds.