Dog training begins virtually at birth. Dogs that are handled and petted by humans regularly during the first eight weeks of life are generally much more amenable to being trained and living in human households. Ideally, puppies should be placed in their permanent homes between about 8 and 10 weeks of age. In some places it is against the law to take puppies away from their mothers before the age of 8 weeks. Before this age, puppies are still learning tremendous amounts of socialization skills from their mother. Puppies are innately more fearful of new things during the period from 10 to 12 weeks, which makes it harder for them to adapt to a new home.
Puppies can begin learning tricks and commands as early as 8 to 12 weeks of age; the only limitations are the pup's stamina, concentration, and physical coordination. It is much easier to live with young dogs that have already learned basic commands such as sit. Waiting until the puppy is much older and larger and has already learned bad habits makes the training much more difficult.
There are some professional trainers who disagree with this idea, particularly those who train working dogs, detection dogs, police dogs, etc. They feel that obedience work shouldn't start until the dog is at least a year old, or after the prey drive has fully developed. These trainers also take the position that spaying and neutering is harmful to the training process, again because of its negative impact on the dog's prey drive.
Next: Dog Training part III - Communicating with the dog