Umm..how do you breed a beagle?

The same as you breed any dog: by talking to local reputable (working, show, and competing breeders who breed for quality, only breed genetically health tested dogs who fit breed standard, and keep their dogs as indoor members of the family) and veterinarians about the subject, doing a lot of research on the breed and possible genetic disorders beforehand, having your dog's conformation tested at an AKC/UKC/Canadian Kennel Club event to see if they fit the breed standard. You can find a purebred stud dog by talking to local show or working breeders who keep strict track of their breeding dogs' papers and lineage, and yes, a dog should ALWAYS see a vet and have genetic health testing and blood panels done before a breeding takes place.