Cacti come in all kinds of shapes, colors and sizes. Perhaps out of curiosity you want to know how best to take care of your cactus, or maybe you just want to know what to tell your friends when they ask you about it. Either way, figuring out your distinct cactus's characteristics will help you down the road to finding it's true identity. Like superheroes, many plants we assume are cacti actually have secret identities and aren't cacti at all. Only careful observation will be able to distinguish the real from the incognito.
Consult a field guide. This is the easiest of methods for discovering the type of cacti you own. Simply look up the characteristics of the cactus in the field guide (types of flower, size, shape, color, etc) and see if you can find a cactus that closely resembles yours. While you may not find an exact match, at least the closest entry will point you in the right direction.
Compare your "cactus" against non-cacti characteristics. Common nomenclature has generalized the specific title of cactus to mean a variety of plants. You know for sure that you have a cactus if the following are true: it has an "aereoles," spines (not thorns), unique cacti flowers, the presence or absence of certain type of leaves, and if it was originally found only in the Americas, or nearby islands.
Search for your cactus on a geographical distribution site, such as is available on cactiguide.com. This will help you pin-point the cactus according to where you found it, and is particularly helpful if you found the cactus in the wild.