As was mentioned, biting is how puppies play. It's also how they learn to gauge appropriate bite force. One theory about the reason for those sharp little puppy teeth is that they are supposed to hurt--the puppy's dam and siblings provide immediate feedback when a puppy bites too hard. Thus puppy learns the appropriate level of force and the amount of nipping other dogs will tolerate much earlier than acquiring the adult jaw strength that can do real damage.
Something also to remember is that puppies need inordinate amounts of sleep, sometimes as much as 20 hours a day during growth spurts. Usually the impulse control fails before the puppy conks out. In other words, a tired puppy is a bitey puppy. I used the toy redirect mode suggested by LMMB. I would redirect to a toy two times. If the biting continued I stepped away for 30 seconds as suggested. If the biting resumed when I returned, I put the puppy into his playpen for a snack and a nap. I made sure to do all of this gently, without a punishing feeling to my movements. Overtired and overaroused puppies aren't in the best mind space for learning and reasoning. Best to just keep things calm so they drift off to sleep as quickly as possible.
The biting you are experiencing with come and go up until about 6 months. It will get much worse when the puppy is teething, which should be done around 6 months. After that the nature of the mouthiness will change. Instead of biting you, your puppy will start chewing on things you leave around. This is another normal stage. Puppies need to apply pressure to their teeth and jaws to encourage bone formation and bone density. This is when you will find the puppy chewing on chair rungs, your shoes, the remote control for the TV, and anything else that strikes his fancy. Keep your valuables out of reach. This stage lasts until at least a year; my guys were destructive until around age two.
