I just got a cat and I wonder what breed it is, how can I identify the breed of my cat?
If you got your cat from a registered cattery, then the breeder should have provided you pedigree papers establishing its breed. If sold as a kitten, the breeder may withhold the papers until you provide proof of spay/neuter; see your sales contract for details. This is the only certain proof that a cat is of a particular breed.
Many breed-specific rescue organizations exist, especially for unusual breeds. Some cats surrendered to these groups do come with pedigree papers (see above). Some do not, but due to these groups' tight focus, it is reasonable to rely on their experience to determine whether the cat is, in fact, of that breed.
Shelters and Vets
Many well-intentioned shelters will advertise stray cats as being of a specific breed (or a breed "mix" or "cross") to make them more attractive to those looking to adopt. Shelter staff may apply the below general techniques, but any claims of uncommon breeds should not be considered reliable due to the staff's limited exposure to them.
Veterinarians may use the same techniques, and their determinations may be more reliable because they have no hidden motivations (you already have the cat!) and because they are more likely to examine uncommon breeds that simply don't end up in shelters, e.g. because they have breed rescue organizations.
Native Regional Breeds
If your region has a breed named after it (e.g. American, British, Norwegian, Siberian, Abyssinian, etc.), most stray cats in that region are likely to be of that breed, either partly or wholly. In fact, breeders from other regions may seek out such "found cats" to diversify a natural breed's gene pool without diluting its distinctive characteristics.
Determine how best to describe your cat's color and pattern, and then check breed standard documents from organizations like The International Cat Association (TICA) and The Cat Fanciers Association (CFA) to find breeds that allow that color/pattern. Many colors/patterns are allowed for several breeds, so while this may narrow the list, you will still need to examine the other qualifications (e.g. head shape, ear positioning, size, etc.) for each possible breed to determine which one best applies.
Mixed or Cross Breed
If your cat does not meet any breed standard perfectly but one clearly better than all others, you may describe it as a "mix" of that breed.
If it meets two breed standards equally well, you may describe it as a "cross" of those two breeds.