Unless the cat has a confirmed pedigree, it is unlikely pet owners can determine the breed exactly. However, the best way to identify breeds for a particular cat is looking at example pictures of possible breeds.
According to the Society for the Prevention of Cruelty to Animals, most cats are either domestic short-hairs or domestic long-hairs, which is based on the length of their fur. However, there are hundreds of cat breeds. The Cat Fanciers' Association features pictures and descriptions of all the pure breeds.
Physical characteristics include ear size, muzzle length, size, tail length and even eye color. Some breeds such as Persians only have certain eye and fur colors. Others such as Maine Coons and Himalayans grow to very large sizes. Manx and American Bobtails both have either no tail or a very short one. Any of these features are prime markers.
Other indicators are the cat's behaviors as certain cat breeds are known for specific behaviors. For example, according to Animal World, Bengal cats are very active and demand constant attention. Ragdoll cats are known for being so affectionate they turn into "rag dolls" with their owners.
For more in-depth information about a cat's breed, veterinarians and breeders can help with identification.