When our shih tzu was a puppy, he would follow closely and bite our ankles and heels with each step...lol. We started yelping loudly (as if in pain) and turning our backs with each nip (even if it was painless). Took about 3 days and he stopped. And get the puppy some squeaky chew toys to play w and some gnawing chews for teething.
Congrats on your new pet.