There have been a lot of threads here about what makes a good breeder and how to find one. Everyone's 'good breeder' metric differs, and some of it depends on what you want the dog for: if you want a chilled family pet, you don't want a Eurohound, and if you want a Eurohound, you're not going to care about KC registration (though you will probably care about the pedigree).
This is going to be long.
The key points are (in no particular order):
The conditions in which the dam of the puppies lives, and where the puppies are born and raised. Clean? Plenty of food and water? Warm enough? Regular weighing? Lots of human attention and some handling? Habituation to domestic noises like washing machines, the radio, cars starting, doors slamming, raised voices, children screeching? Things for the puppies to do - cardboard boxes to climb in and out of, different surfaces to explore, the odd toy? What food are the puppies being weaned onto? Have they been brought up with other dogs around? (Our youngest dog was 'nannied' by the other bitch in the house, and she has a rock-solid temperament now.)
Temperament: how does the dam seem when you meet the litter? Are there any other related dogs around that you can see and interact with? Can you contact the owner of the stud if you want to? How does the breeder interact with the dam and what she is like in return?
Health: dam and puppies in good shape? Has the dam been health tested for any conditions prevalent in the breed? If she hasn't been, has the stud - you don't need to health test both parents for genetic illnesses that are simple recessives, because carriers will not be affected. If a breed has generally good hips, and the stud has a low score for hip dysplasia, and the dam hasn't been tested, you'll need weigh up if that is a risk you're prepared to take. There is a lot to think about here, and some of it is breed-specific.
Co-efficient of inbreeding: Ideally, below 5%. The higher the COI, the higher the risk of genetic illness (including ones that cannot be tested for or have not been identified) and immune problems. If you get the pedigree names of sire and dam, the KC website will calculate the COI of any puppies for you - just google 'Kennel Club mate select' and you'll find it).
KC registration: if a pedigree puppy is not KC registered, I would query why. It's a cost the breeder can recoup in the sale price so expense is not an excuse. It might be that the dam has had too many litters for any further ones to be registered, or that she was 'endorsed' by her breeder, which means that none of her progeny can be registered unless her breeder lifts the endorsement. Breeders often do this to cover things like health (the dam must have passed various health tests) or working ability (she must have won a field trial, for example).
What sort of dog you want your puppy to be: if you want a chilled family pet, you don't want a working cocker out of field trial winners or need a labrador who parents were both placed at Crufts. The parent dogs need to be thoughtfully matched, healthy (and health tested if relevant) and of sound temperament, and the puppies well brought up with plenty of human interaction - that is really all you need. The idea of only breeding show winners just serves to further narrow already narrow pedigree gene pools. You do, though, want the parents to have sound conformation, and if you're not confident that you can assess this yourself, it's as well to see if there are show-winning dogs in the recent pedigree, or workers who have gone on in the field over the age of ten.
How do you find breeders like this? Everyone always says via the breed clubs, but you can also find excellent breeders on ChampDogs. There are even some decent ones on pets4homes - though that is a minefield and you need to be pretty confident about what to look for and what questions to ask, because a lot of puppy farmers (and puppy smugglers) are bloody clever and determined and will go to extreme lengths to convince you that they are legit breeders of their lovely family dachshund...
And ask questions. Ask lots and lots of questions. Why did you want to breed the bitch? How did you select the stud? How much do you handle the puppies? What influenced your choice of weaning food? Will you breed the bitch again? Why? Have you got any photos I can see of her before she had puppies?