It is not unusual for a puppy to bite during play but it should always be discouraged. Giving a sharp "NO!" and ending the play should be enough. If your pup is overly agitated a time out may be in order. Never hit or be rough as that can incite even more aggressive behavior.
There have been some very good instruction about the subject posted here by people with a lot of experience with dogs.
Gracie was a live wire when she was a puppy but not as bad as some of the circumstances I have seen posted here.
If you have a very excitable puppy sometimes it is best not to let them get to the point where they will bite. Try to keep them calm and don't move your hands in front of them because that means play to them and as puppies play means using the mouth and teeth.
Lots of exercise is always a good idea. If you can't go outside for a long brisk walk teaching the pup to play indoor fetch is great exercise as well as just running around the house or apartment. A tired puppy never bites.
