Instructions
Take a very close look at the error. Use a magnifying glass to determine whether the coin is actually an error, or if it has simply incurred scratches and dents during the time it was in circulation. If the coin is a proof or uncirculated coin, do not remove it from its protective holder.
Consult both coin pricing guides and error guides. Some errors are very well known and will be found in price guides. For instance, the 1955 double die Lincoln penny is a valuable and well-documented error that is found in every price guide. Other errors, such as those found in the more recent state commemorative quarters, are not as well known. In that case it pays to read coin magazines like Coin World and consult online error columns. If you still cannot find the error, you may have something truly unique. Ken Potter, a columnist for Coin World, maintains a blog that keeps track of error coins.
Send the coin to a reputable grading service. The two most widely respected grading services are PCGS and NGC, but there are other grading services as well. Note that there is a charge to have a coin registered, and if the error is a common one that isn't worth very much, it may not be worth it to have the coin certified.