Those needle-sharp puppy teeth can hurt and draw blood. One puppy owner even made the comment that after one play session, she could have donated blood.
Unfortunately, wounds like that shouldn't happen. Keep in mind dogs (and puppies) repeat actions that are rewarding to them and if playing with you (and biting you) becomes fun, then stopping the behavior is going to be that much more difficult.
Thankfully, stopping puppy biting doesn't have to be difficult.
Your Hands are not Targets
Ideally your puppy should see your hands as wonderful things that provide food, give treats, pet softly and offer toys. The source of wonderful things should not, then, be a target of biting.
To make sure your hands are not a biting target, don't instigate rough play. Don't wrestle with your puppy which will cause him to fight back and bite at your hands. Don't wave your hands in front of his face or what I call finger fighting; messing with his face with your hands, wiggling your fingers in front of him, or otherwise tease him. It's important, too, to resist putting your hands (or fingers) in his mouth when playing or interacting with him.
Focus on a Toy
When I have a puppy at home, one of the first things I teach him is to find a toy when he wants to play. If he's focused on a toy then he's not targeting my hands.
The phrase I use is, "Get a toy!" and when he has a toy I praise him. This makes my dogs happy and they know I'm pleased with their choice.
To teach this, have some soft, chewable puppy toys within reach any time you're interacting with your puppy. When he wants to play, offer the toy before he tries to target your skin and tell him, "Get a toy!" and wiggle the toy so he's attracted to it. When he grabs it, praise him.
Sound Like a Puppy
In a litter of puppies, when one bites another too hard, the puppy being bitten is going to immediately react. This high pitched verbalization tells his littermate that he's biting too hard. Although the game usually continues with the biting puppy being more gentle, if the biting continues to be too rough, the puppy being bitten will cry even more which usually brings the mother dog to break things up.
Although you'll never sound exactly like a puppy, you can use a high pitched voice to let your puppy know what he's doing wrong. When the puppy touches you with his teeth, say, "Ouch!" in a high pitched tone of voice. React quickly and loudly; don't hesitate. You need to make an impression on your puppy. When he looks startled, offer him a toy and when he grabs it, praise him.
Stop the Game
If your puppy bites you during play and doesn't stop when you say, "Ouch," stop the game immediately, get up and walk away. Don't hesitate and don't give your puppy a second chance. To make this work you need to be decisive and make an impression on your puppy. Your message should be, "If you bite me, the game is over."
If your puppy chases after you biting at your shoes, feet, ankles or pant legs, put him in his crate and give him five to ten minutes to calm down. Don't yell, scold, shake a finger at him or otherwise punish him. Instead, you want him to calm down and relax. Then let him back out of the crate.
Consistency is Important
Puppies don't have hands (even though their paws manipulate items well), so they try to control their world using their mouth. Play biting is normal between most puppies and dogs, and they are great about teaching each other when one is too rough. Because people are often inconsistent about communicating with the puppy, some puppies have a hard time learning that they aren't allowed to bite people.
Talk with everyone involved with the puppy and establish guidelines. Make sure everyone knows how to verbalize to startle the puppy, offer a toy and when to stop the game and walk away.
Emphasize the importance of stopping the behavior now, when your pet is a baby, rather than waiting until he's a dog who could hurt someone if he bites.