According to The Dog Owner's Guide, the majority of dogs in the world are mixed breeds. This means that, unlike purebred dogs, they have more than one breed in their bloodlines. While there are standard mixed breeds that are easy to identify, such as maltipoos, most mixed breeds, or mutts, are more difficult to decipher. These dogs may have more than two breeds in their makeup, or they may be an unusual combination (such as a papillon/dachshund mix). Even if this is the case, there are several ways to determine at least part of a mixed breed's ancestry.
Compare your dog's appearance to that of standard breeds. Often a mixed breed will show at least one distinct characteristic of the breeds in its makeup. A chow mix, for instance, might have black spots on its tongue.
Watch your dog's behavior, and compare it to standard breed behavior. A dog with terrier in it, for example, may enjoy chasing rabbits.
Purchase a DNA analysis kit. Different brands of these kits are available from many pet supply stores. They allow you to swab your dog's mouth and send this sample to a lab for analysis.
Ask your veterinarian. Vets see hundreds of dogs a year and are often able to spot similarities among various breeds.