You need to nip this one in the bud, immediately. A nip will turn into a bite.

The problem with harsh corrections is that some dogs will get scared and bite for real because they're frightened. Dominating and causing pain in the dog's mouth can cause more serious and aggressive behavior or fear-biting.

First, you need to enforce no bite. That means you, the kids, the spouse, etc. cannot allow the puppy to nip or even put a teeth on you. The moment your pup starts nipping, remove yourself and your hands, turn around and walk off. If he follows you nipping, command him into a sit or down. You can make a displeased noise or the command "no bite."

Once your pup stops nipping or biting, you can quietly praise him and give him something to chew like a toy or a chewie.

The idea is to take away the fun and attention when he nips, substitute an alternate behavior (sitting or lying down) and giving him praise when he doesn't nip or bite. I highly recommend that you take your pup to a positive reinforcement obedience class.

Good luck with your pup!

I treat no breed of dog specially, terriers to poodles to, well, our Rotties. "Nipping" (aka biting) people is not allowed. The trick is that EVERYONE - including the kids - has to be consistent about not allowing it. He can't nip some people, or just clothing, nothing. Everyone has to express disapproval. It usually takes the form of a sharp "No" and dominating in some way - Cesar Milan does this well.
We sometimes banish our dog to his "kennel" for a few minutes of shunning (kennel is a rug in the corner of the living room) until he's calm and ready to hear.
When a pup starts chewing on our hands, we often worm two fingers (no long fingernails!) into their mouth and depress the back of their tongue until they gag - not choke, we don't push down their throats and are careful not to scrape along the way. As we do this, we calmly say "Ouch". Later, this morphs into "Out". Our dogs are pretty good at spitting out anything when they hear this. This is more for chewy behavior than biting, but it might help as well. BE CAREFUL, and be calm.
Enjoy making the little guy part of your family!

From BostonTerrierSavvy.com - Stopping Boston Terrier Puppies Biting
When boston terrier puppies nip at your skin produce a sharp cry. The more you can make this sound like a high pitched yelp the more he should respond to it. Yelping is what his other four-legged brothers and sisters would do, so it is more likely to work to your advantage as he is more apt to respond on instinct.

I agree with skywarrior, above. Don't overdo the correction, just remove yourself (and any toys that were involved) from the dog for at least a few moments - the message being "if your tooth so much as touches me, fun time is over".

People make the mistake of being too harsh in trying to assert themselves as the alpha. In the extreme, this can actually make your dog fearful and unstable.

You're smart to be addressing this now. Too many people let puppies get away with behavior that would be unacceptable in an adult dog, which just makes things harder in the long run.

ALSO - AND THIS IS VERY IMPORTANT (sorry for yelling, but it really is!) teach your kids to behave appropriately with your dog. Don't blame the dog for biting the child if, say, the child was yanking on it's ear or trying to stuff an ice cube up its nose. Dogs can't say "stop it", so they use their mouths. It's natural dog behavior.

Remember, we're wired like monkeys, dogs are wired like wolves. The better we learn to understand each others' languages, the better we can live together. - see "The Other End of the Leash - why we do what we do around dogs" by Patricia McConnell. It's entertaining and enlightening.