All puppies bite, this is normal behavior for puppies. Puppy play-fighting and play-biting is how your puppy learns to develop a soft mouth as an adult, with your help. It is likely that you have watched a litter of puppies in play. Those guys get really rough, the jump on each other's backs and grab a hold of the neck with teeth and really bear down and shake their heads. Just like children in play, sometimes things get out of hand and a pup will bite too hard for the one that it is on the bottom. What happens? The offended pup yelps and takes off. In dog language, the offended pup is saying, "you are too rough for me, and I am not playing if you are going to be so rough". You are going to use this same dog behavior language to teach your dog to play bite nicely.
We are not going to expect the pup not to bite, it is going to bite (all dogs bite), but we are going to teach him that when he uses his mouth, he is going to do so softly. We call this bite inhibition. Every time your puppy puts his mouth/teeth on you, you are going to give a yelp/sharp quick scream and then leave, thus ending the play session. After a minute or so, return to your puppy, take a soft chew toy with you, and resume playing. Since all puppies love to play, every time you play and leave when your puppy puts it's mouth on you, the puppy starts thinking, 'man those humans are sure sensitive, if I want to keep playing, I am going to have to play nicer. Gradually, through repetition and consistency, you puppy is going to learn that in order to play, he is going to have to keep its mouth to itself.
Never allow your puppy to mouth, hair, shoes (laces), pants, legs and toes this inadvertently teaches the puppy that it is okay. If your puppy is biting at anything on your body, stop playing! Walk away, if it chases you still biting at your pants, pick it up and take it to a small room (washroom, bathroom) or pet carrier. Time out. Go back in a minute and start again. If he persists, you persist. Keep putting puppy alone by itself until his biting behavior stops.
Consistency is important. EVERYONE IN THE HOUSEHOLD MUST FOLLOW THE RULES!! EVERY TIME!! Failing to do this give the puppy mixed messages and will not help him learn what is expected of him. The rest is repetition. With time and maturity your puppy will bite less and less and softer and softer.
Watch this video on puppy biting