Around 12 weeks old, a puppy should get his second set of shots. In this set, your puppy should get the DHPP and possibly the Bordatella vaccinations. He will still need one more set that will include Rabies, usually done around 16 weeks of age.
That depends on a few factors the vet you have will be able to tell you what order they will go in because it depends on the age and weight of the dog the closeness of the shots the dog has already had and how quickly you want it done.
Second set of shots should be given at the age of 9-11 weeks and are called DHLPP+Corona. These protect against distemper, hepatitis, leptospirosis, parainfluenza and parvovirus.