Redirecting the Bites
Every time your puppy puts his teeth somewhere he shouldn't, you want to redirect him to something he is allowed to chew on, such as a toy, and then praise him. This sets him up for success by learning which objects on which he is allowed to chew.
When he chooses to chew on your hand or clothing, which he inevitably will, yell "ouch!" and storm away from the puppy as if you are angry, even if the bite didn't hurt. Leave the room and shut the door if necessary. Puppies playing together in a litter do the exact same thing to teach one another how hard is too hard for a dog bite. When a puppy bites too hard, all the other puppies will turn their backs on the rowdy pup and isolate him. As your puppy's "pack," you must do the same thing. The most effective way to stop puppy biting is too isolate your puppy every time he bites. If you do this consistently (every time) the puppy biting will stop.
Include All Family Members
If biting works occasionally to get attention, your pup will try every time, just in case this is the time it works. If it always results in complete isolation, it will stop almost immediately. This requires participation from everyone in your family, especially your children. If the puppy is nipping the kids while they are playing, tell your children that as soon as the puppy nips, they must stop the game and storm from the room. This will have a big impact on the puppy.
Alternative Methods
If you are too busy to storm out of the room every time your puppy bites, keep a small, thin leash on him while you are home. If your puppy bites, use the leash to lead him quickly to his timeout spot. After saying "ouch!" don't talk to him or touch him while you do this. The timeout spot can be a crate or small, quiet room. Don't let him out until he has calmed down. He may just need a nap.
There are also several sprays available that discourage chewing. Some dogs are not affected by these sprays, but if yours is, spray some on your hands right before playing with your puppy. Spray it on yourself near your puppy so they get a big whiff of the bad stuff and are encouraged to stay away from it.
Whatever method you choose, remember that consistency is the key! React the same way every time, and your puppy will stop biting quickly.