The value of an old coin depends on its condition, denomination and country of origin. One 1818 coin may be worth much more than another 1818 coin due to any combination of these factors. Two 1818 coins minted on the same day in the same denomination may be worth drastically different amounts depending on their condition. The best way to determine the value of your 1818 coin is to grade it, then look it up in a price guide.
Identify the coin. Look for a marks identifying the denomination (quarter, penny, half dollar, etc) and country of origin.
Grade the coin.
Look up the value of the coin.
Take the coin to a dealer for a more exact value now that you have a ballpark idea of the coin's worth.
Grading criteria varies with different coins, but there are four basic categories. A good coin is very well worn; its date and information are readable, but its images are difficult to discern. A fine coin is well worn, but its design is intact. An extremely fine coin has light wear and looks very nice. An uncirculated coin is in perfect condition. There are more than the four basic grades, but these are the easiest to define broadly. Coin price guides have greater information about grading specific coins. Coin price guides specialise in types of coins (U.S. coins, foreign coins, etc). They are available at most book stores and coin shops. Online price guides exist, but they are not as well respected as their print counterparts. Most coin dealers will give you an honest estimate, but you should always research the coin's value before visiting a dealer.