I'm getting a puppy at the end of the month, so I've been doing a lot of reading up on problem behaviours and how to combat them (not that it makes me an expert in any way, shape or form). Here's something I found in one of my books to teach your dog that you don't like to be nipped.
Puppies use thier mouths to investigate things, much the same way humans use their hands. They also use their mouths in play, and sometimesk, to vent their high spirits. But needle-sharp teeth hurt, so puppies must be taught that nipping isn't nice.
Caution: Resist the urge to jerk your hand away from your puppy when he clamps down on it. That's the canine version of an invitation to play, so pulling away just makes him come back for another nip.
It's fine to pet your puppy as he licks and mouths you, but if he clamps down with his teeth, tell him it hurst. How? Say OUCH! And say it like you mean it. Screech it out ina high pitched voice that lets them know that he/she hurt you. Most pups lick you in apology. If a week or two of yelping OUCH doesn't make a different, use a different command that means "Don't bite". Then say it every time he touches you with his teeth, while putting your finger on his button nose and pressing gently. The last resort is dabbing Bitter Apple ont he part of you your puppy nips. It works especially well on sock and shoelace chasers.
I hope this helps you a little. I'll be trying it out on mine too, if it's a problem....