Type
Different types of coins are generally worth more than other types. An old half dollar, for example, tends to be worth more than an old nickel because of the materials used to make them. The larger the denomination, the more the old coin is likely worth. Country of origin is also important when determining the value of coins. All of this information is usually printed on one of the faces of the coin. There are also specific types of coins--buffalo nickels, for example--usually referred to by the image on the front or back of the coin. Coin stores and collector guidebooks are a good place to learn about the specific coin types.
Mintage
Mintage refers to the quantity of the coin made. Obviously, the fewer coins made, the more valuable they are. Mintage numbers depend mostly on perceived need from the government's end. Some countries mark the specific mint where the coin was created on the coin itself with a small letter.
Condition
The condition of a coin is what makes one coin specimen worth more than another specimen of the exact same coin. Coin conditions for circulated coins range from about good (the lowest) to uncirculated (the highest). Specific coin grading criteria differ greatly from coin to coin, so it is a good idea to buy a coin price guide specializing in the type of coin you collect to learn more about grading and the values of a specifically graded coin.
Demand
The selling and buying of old coins follow trends like the selling and buying of any other collectible. Because of an event or shift in the market, some old coins will be worth more at one time than they would be at another. In general, specific coin types come into demand all at once. This information is easiest to follow by going to coin shops and auctions, and by talking to other numismatists.
Errors
Errors in the physical appearance of a coin can also greatly affect its value. Errors can be anything from the image being offset to actual chunks missing from a coin. In some instances, like the 1955 double die Lincoln head penny, on which the date was struck twice, creating a mirror image, the die can greatly increase to worth of a coin. Again, coin guides are an excellent place to learn about specific errors and their affects on the value of coins.