Genetic blood test.
You can DNA match the puppy to the Sire/Dam if you know they are pure bred and that is a question. There are some commercial doggy DNA tests but not all have all breeds and they are not known to be completely accurate at this point (pretty hilarious a lot of the time actually) for the most part though they will probably improve on them as time goes by. The more expensive tests can be a little more accurate. For now they are more for entertainment. Sometimes they are right and sometimes not or just not possible. To accurately DNA test you still kind of need to know what they are still at this point but we're getting there. The first link is a link to a DNA test on a dog whose lineage is known (what is with the tendency for black dogs to come up with border collie even when absolutely not I don't know). Not only is the dog an actual pure bred with verified lineage, well, watch to the end. :-)
For now the best way if pure bred is a concern is still to look for a pup with AKC or similar for country registration or breed parent club if an actual breed that has been around for hundreds or thousands of years (can be confusing with all the ones popping up because it suits purposes). Not a 'paper' or pet registry. You can also see how well your pup measures up to the breed standard but just because they don't doesn't mean they aren't pure bred, just they couldn't compete in or win a show in many cases. It isn't the most accurate way but could help. Some breeds are more commonly mixed and represented as pure bred than others (like Pit Bulls/Am. Staffs ect.
www.youtube.com
www.akc.org www.ukcdogs.com
www.dogfoodanalysis.com
For now the best way if pure bred is a concern is still to look for a pup with AKC or similar for country registration or breed parent club if an actual breed that has been around for hundreds or thousands of years (can be confusing with all the ones popping up because it suits purposes). Not a 'paper' or pet registry. You can also see how well your pup measures up to the breed standard but just because they don't doesn't mean they aren't pure bred, just they couldn't compete in or win a show in many cases. It isn't the most accurate way but could help. Some breeds are more commonly mixed and represented as pure bred than others (like Pit Bulls/Am. Staffs ect.
www.youtube.com
www.akc.org www.ukcdogs.com
www.dogfoodanalysis.com