Puppies can't help having the urge to nip and chew. They use their mouths to communicate, to explore the world and to interact with other dogs. When they start nipping at you, though, you need to correct them right away. When you let a puppy nip you, she learns that it's acceptable, and she'll keep on doing it into adulthood. If you nip it in the bud, as it were, you'll quickly teach her that using her mouth on people is never the answer.
Engage in normal play with your puppy, and keep a chew toy at the ready. You'll need to have it handy when she nips, and the only way to teach her not to nip is to show her the consequences of doing it.
When she nips or chews on you, immediately pull your hand back and make a high-pitched yelp. Even if it didn't hurt, you need to teach your puppy that it did. What she learns is called bite inhibition, and it's the same basic thing she learns from playing with other dogs: If she bites too hard, she's going to accidentally hurt someone. Your puppy doesn't want to hurt you -- she just wants to play. When she sees that you've been hurt by a nip, she starts learning to not do it.
Give her an appropriate chew toy to chomp down on as an alternative to your hand. Praise her when she plays with it.
Repeat this every time that she nips or chews. Eventually she'll understand the pattern and stop. Puppies only learn a pattern if it's consistent, though, so you have to do it every single time she nips. If she still doesn't stop, get up and leave the room, going where she can't follow. Don't come back for 10 minutes. Again, be consistent with this step -- if she learns that biting leads to playtime being over, she'll stop.