It used to be that trainers and veterinarians recommended that puppies begin training classes as soon as they were old enough to have all of their vaccines and boosters. What this meant was that some puppies didn't get to class until they already had behavioral issues and were headed down the path to a problem that started in the Critical Period of Socialization or Fear period.
As a result, veterinarians, veterinary technicians, animal behaviorists and many trainers now recommend that puppies (who do not have health problems) begin classes as early as 7-8 weeks.
The American Veterinary Society of Animal Behavior (AVSAB) states: "In general, puppies can start socialization classes as early as 7-8 weeks of age. Puppies should receive a minimum of one set of vaccines at least 7 days prior to the first class and a first deworming. They should be kept up to date on all vaccines throughout the class."
The idea here is that inadequate socialization during the first two to three months of the puppy's life can result in behavioral issues (including fears, phobias, avoidance, and aggression) that extend well into the dog’s life. For more see the complete Position Statement on Puppy Socialization.
While there may be some breeders and trainers who disagree, the current thinking in the medical and behavioral world is that the benefits of attending classes early outweigh any possible health risks.
In AKC S.T.A.R. Puppy classes for young puppies, instructors will tailor the instruction for the age of the puppy. Most of the class in the beginning will be geared at play and socialization. By the time the puppies graduate 6 weeks later, they are developmentally ready to begin learning additional new skills.
Adapted from: AKC S.T.A.R. Puppy: A Positive Behavioral Approach to Training Your Puppy (Dogwise Publishers, 2013). Find a dog trainer near your location and take the Canine Good Citizen test for your dog.