Instructions
Look for the Lionel name or logo printed along the side of the engine or train cars. Look for the numbers printed on the side of each train, and cross-reference them with an online train collector database or collector book.
Examine the tracks that came with your train set. Check the website "I Buy Old Trains" (see resources) for a list of trains and their accompanying set of tracks. You should be able to determine the type of tracks from the distance between rail ties.
Find a local hobby shop that deals with model trains. If they have someone with expertise in model trains they may be able to help you identify your set.