How do I get my puppy to stop biting?

A firm “NO” when he/she bites.

First, don’t panic. All puppies do that, as you said, and you can very easily teach them not to.

You have to be CONSISTENT and make sure everybody does the same.
It’s important not to give her any attention when she bites – if you are playing and she is hurting you, tell her a firm NO and stop all play for 5 minutes, if possible ignoring her or taking her out of the room. After she has calmed down a bit, you can resume play or whatever you were doing before she started being mouthy.
But as I said, you have to be really consistent and do this no matter what – if you don’t, it will take a lot longer.

Spanking or beating her is not a solution to this problem, so no matter what other say, you shouldn’t do that. You can seriously traumatize a pup for life if you do that.

This site offers a very detailed description of the right method. It’s really useful to read:

When ever it gnaws at you kinda push it away and scold it with a stern no. However if you don’t use a different tone while using no he won’t be able to tell the difference.

Puppy biting is a normal, natural, and necessary puppy behavior. Puppy play-biting is the means by which dogs develop bite inhibition and a soft mouth. The developing puppy should learn that his bites can hurt long before he develops jaws strong enough to inflict injury. The greater the pup’s opportunity to play-bite with people, other dogs, and other animals, the better his bite inhibition will be as an adult. For puppies that do not grow up with the benefit of regular interaction with other dogs and other animals, the responsibility of teaching bite inhibition lies with the owner.

Check this link for more guidelines.