It's truly never too early to begin training your puppy. Some training, such as housebreaking, cannot be reliably completed until the dog has full control of his bladder or bowel, while more simpler feats can be trained while the puppy is still very young.
Puppies between the ages of 3 and 14 weeks of age are curious and willing to discover new things. This is a critical time for socializing a new puppy, so teaching a puppy to be comfortable around new people, places and things should begin when the puppy is just about a month old.
Be aware that until puppies are fully vaccinated, they should not be around other dogs unless in a controlled environment, such as a professional puppy kindergarten class, to avoid communicable diseases and parasites.
Basic training skills such as sit, stay, come and heel can begin at around 8 weeks of age. Sessions should be short, only about five to 10 minutes twice a day in the beginning, to accommodate a puppy's short attention span. Increase the training sessions a minute at a time to a maximum of 20 minutes twice a day.
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Housebreaking training should begin at about 8 weeks of age. Some dogs will catch on very quickly, others may take longer. Dogs cannot control their bladder or bowels for more than a few hours (one hour for each month of age), so taking him out every 20 minutes or so is critical.