I think training starts from the moment the dog is in your household. Although it is obvious you won't ask a 9 week old puppy to heel, but you sure can start training him not to bite and do his business outside. Gradually the sit and down commands are taught and shortly you'll be training tricks. :dogsmile:
I've known of some border collie breeders that start teaching simple commands as early as they can see and walk. According to them, it goes wonderfully and gets an early start on the pup's training. At 8 weeks their pups leave knowing sit, down, stay, shake, and a couple of other commands I think. The earliest I've ever started was 8 weeks, which is when I got a puppy a loooong time ago and no longer have.
For assistance dogs, it is becoming common for programs who breed their own litters to start training, like tx_cowgirl said, as soon as the pups' eyes open and they begin to play - before they can hear noises. That is around 3.5 weeks, depending on the breed. The puppies I have worked with typically know close to 60 commands by 16 weeks of age.
As long as you keep learning short, fun, and always successful you can't go wrong
I started with Karla as soon as we got her at 7 weeks. We've only been at it for 2 weeks now, but she is absorbing everything I teach her. I keep it short and fun. She comes back to the whistle (even while being distracted by my husband), and knows the clicker and luring, we're starting on the sit which she is picking up very quickly. She even walks to heel, even though she can only walk around the garden at the moment. I think the sooner you start the better and can highly recommend printing the lessons from here and working through them.