Be aware that all dogs need to chew, especially puppies. Make sure that you have lots of appropriate items around for him to chew on. To teach him that your body is not an appropriate item, this is the method that I recommend:
When puppy takes your hand in his mouth, tell him no (not too loudly or you might add to his excitement) and redirect him to something appropriate to chew on. When he bites hard enough to hurt, you need to let him know. Yelp loudly, immediately break eye contact, stand up and turn your back on him for 30 - 60 seconds. After that time, all is forgiven. In this way, you teach your pup what is called "bite inhibition".
Be sure you have lots of chew toys and bones for him to chew on. Puppies NEED to chew. When he is chewing on something appropriate, PRAISE him heavily and drop a small treat. Always reinforce good behavior. Behavior that is rewarded increases in frequency.
Also be sure that he is getting plenty of exercise. As they say, "a tired puppy is a good puppy".
Good luck! This too shall pass.
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