I am a purebred dog person. I show and compete in performance events with my Brittanys Biddy and Tristan. Some people want a purebred dog - and the question becomes how do you find a reputable breeder out there in a sea of puppy mills, backyard breeders and other not so well intentioned people?
The best breeders are typically not advertising and not popping up on internet searches. That space is usually reserved for the worst. A great place to start is the breed club for the particular breed you are interested in.
Every breed out there has a National breed club, with many regional or local chapters. I suggest this over just someone who has a registered kennel, since just about anyone can register a litter or a kennel name. As a general rule, those that are involved with a breed club are doing one or two things actively with that club. They are either actively competing in conformation events (the AKC dog show) or performance events specific to that breed -field trials, hunt tests, scenting events, herding or in a lot of cases both conformation and a breed specific performance event.
These are the people that you want to connect with when looking for a dog of that breed. These are the people that have devoted a lifetime to a particular breed. They are willing to talk to you for hours about their breed, what is good about it, and what is not so good.
So for me, this begs the number one question you should be asking a potential breeder...why? The answer should be for the betterment of the breed. If as a breeder you are not actively exhibiting your dogs at an AKC sanctioned conformation event to determine how well they conform to the standard of your breed...why are you breeding? Or, if you are not participating with your dogs in sanctioned performance events that are specific to your breed, again...why are you breeding? If you don't have your breeding stock evaluated in either a conformation event or sanctioned performance event, how do you know? Why are you breeding? If as the breeder you aren't participating in one or both if these things...you are sadly just breeding to breed...or as a business.
In my mind, the breed club is the place to start. My experience has been and continues to be that the people that are active in the breed clubs know one another, know one another's lines and are happy to share information and help you find the right breeder for you. There typically isn't room for someone in a breed club that isn't actively exhibiting in either conformation or performance events - period the end.
Breed clubs have gatherings all over the country to celebrate their breed. These are typically National Specialty shows (conformation) and national breed specific performance event championships. These are the people you want to connect with when you are looking for a purebred dog. They are typically NOT the ones advertising puppies for sale. A new dog is a lifetime decision and breeding is a huge responsibility. There are a lot of really good breeders and AKC Breeders of Merit out there. Typically a search for (fill in the breed) puppies will not lead you to those people. Search out the breed club of the breed you are interested in. Start talking to those folks about your breed...you will learn a lot and hopefully get closer to finding the right breeder for you.
Be prepared though...puppies are usually not readily available, there may be a significant wait for a puppy. Be prepared to demonstrate how you will take care of the puppy, and if you are not agreeing to show..to prove that at the right time you have indeed spayed/neutered your dog. Be prepared for a list of conditions and circumstances that are unacceptable to the breeder and to agree to give the dog back if you can't take care of it before turning it over.
Be prepared to connect with someone who will be happy to always be a resource for you on your dog for the lifetime of your dog, who is always happy to see your puppy pictures and celebrate milestones in your dog's life. There are a lot of outstanding ambassadors of all breeds out there...they are just a little harder to find. You can find a complete list of all the breed clubs in the country on the AKC website.