(Welcome to another informative and exciting edition of Investing 101! We're going to go a bit beyond the basic investment classes like stocks and bonds, and into some of the more exotic investment and speculation opportunities. Our subject for this article is options.)
Q: I keep hearing about options in the media, but what are they, anyway?
A: In a nutshell, options are financial instruments that allow the holder to buy or sell an underlying asset (usually, stocks) at a price other than the current going rate. Because they depend on other asset classes, options are considered derivatives. The price changes in the underlying assets affect the value of the options.
There are two different styles of options, which influence when they can be exercised (that is, when the option-holder is allowed to buy or sell the underlying asset). American-style options can be exercised at any time the holder desires, while European-style options can only be exercised on the date of expiration. (All options have an expiration date, but American-style options can be exercised before that date if the option holder chooses.) American-style options provide the holder with more flexibility, while European options allow the seller to be certain of when the options will be executed.
Q: Okay, I follow so far. What types of options are there?
A: Options come in two basic flavors, depending on what they allow you to do with the underlying assets. Call options enable the option holder to buy the asset from the seller at the strike price, the agreed price set out in the option. The call option seller agrees to provide asset at the strike price. If the strike price is below the current market value, the option is considered to be in the money, and the option holder can exercise the option and purchase the asset at a discount to its current market value. If the strike price is above the current market value, the option is out of the money, and it will expire without being activated.
Put options are just the inverse; the option buyer has the right to sell the underlying asset to the option seller at the strike price, regardless of the current price of the asset. If the market value of the asset falls, the option buyer comes out ahead, selling the asset to the option seller for more than it is current worth. Conversely, if asset value rises, the option will expire without being acted upon.
Q: That's all a bit complex. Can you help me to sort all this out?
Of course. Here's a chart that should clear some things up:

If we look at this table, we can see that an call option seller, for example, wants the asset price to fall below the strike price; in that situation, the option would expire out of the money, and the seller would be able to keep the option price without having to sell the underlying asset.
Q: What are the risks with options?
The risks vary, depending on whether you are the buyer or the seller. If you are buying options, your only real risk is that the option will expire out of the money. In that situation, you will lose the money you put up to buy the option, but that's it; your liability is limited to the option cost.
For the seller, however, it's a different story; if the option expires in the money, you could be forced to sell your assets at prices below market value (for calls) or to buy assets at an inflated price (for puts). As a result, the risk level for option sellers is much larger than buyers.
Q: How should I use options?
A: Sparingly, at least until you have a better handle on the risks of various option strategies. If you decide to invest in options, keep them to a small portion of your overall portfolio. Be aware that the amount you can lose from option investing can go beyond the amount of money you initially put up, particularly when selling options, and make sure that a bad options bet won't damage the rest of your portfolio.
This article has just scratched the surface of options and option trading strategies. There's a vigorous market in options, just as in stocks or bonds, and the price of a particular option contact will be affected by the value of the underlying asset, the time until it expires, and the volatility of the market, among other factors. And there are numerous strategies, like ‘straddles' and ‘strangles' that I haven't mentioned. But for now, I hope this helps you to have a bit better understanding of options.