All dogs bite

It starts as puppies exploring the world with their mouths. Puppies also bite to relieve the discomfort of teething. Sometimes, play biting is a sign of fear or confusion. Puppies may also bite to initiate play. The most common and serious type of puppy biting is fear biting. The most common type of puppy biting is called "play solicitation" or "asking for play by nipping."
 

The goal is not to stop all play but to teach the pup to bite toys, not you, and to learn games that don't involve play biting such chasing a ball.

Play is important to healthy puppy development.

If the puppy learns that play biting works as a way to get people to play, then the puppy will tend to bite more. Nature insists that young puppies play for exercise and building their muscle, nervous system, and respiratory organs.

The goal is to teach the pup to bite toys not you and to play games that don't involve play biting such chasing a ball or Tug-of-War with rules.

Do not scold the puppy for play biting.

Do not respond to play biting by scolding or in any way physically reprimanding the pup. This tends to make the play biting worse as the pup seems to think you are initiating rough play.

The best response to play biting is to pretend you are a puppy. When the puppy nips or bites you, yelp and cry like a puppy. As soon as the puppy backs up, count to 3 or 4, and then praise the puppy for stopping the biting. Then immediately offer your hand again for gentle mouthing.

If the puppy licks instead of bites, praise that. Allow the puppy to mouth gently for the purpose of learning how to be gentle. As the puppy becomes more excited and bites with more pressure than allowed, yelp again, as if the teeth have mortally injured you. 

The goal is to intentionally startle the pup and stop the play biting Then, stop playtime and turn your back on the puppy for several seconds, or until the puppy has calmed down.

 Stopping the joy of playtime is the best reprimand for puppy play biting.

Tough love

If the puppy does not back off when you yelp, then double or triple the volume and the intensity of the yelping until the puppy seems startled. If this fails to stop the biting, discontinue all play and leave the room.

Repeating this response gives the puppy the best chance to learn how much pressure it takes before the yelping starts and the play stops. This process teaches "bite inhibition."

The puppy learns to inhibit the pressure of his or her bite well below the threshold of real pain to people so that later, if the adult dog is hurt, a natural response will be to give a soft, warning bite instead of a hard bite.

The adult dog will remember the puppy lesson that people are so delicate, that just a little pressure will make them crumble.