You can start to lay a great foundation at home at this age, but I know that where I work, we won't take puppies until they are 16 weeks of age, due to shots. But you can start working on sit, stay, down, come, leash manners, off, and a host of other things to get your puppy interested in learning.
Clicker training can be very fun for a dog this age; the game 1001 things to do with a Box is a great place to start. First, get your dog acclimated to the clicker so that it equates "click" with "I did something good". The reward can be either praise or treats. Then just set a cardboard box down in front of the puppy and see what it does. Reward for any interest in the box at first, then see what little things the puppy does on it's own. When you see something you like, click to that and treat, come up with a command name for it and work on shaping it.