I could make a very long post about this but there are a couple of things you need to be aware of.
1. It's a good thing when puppies bite. However, they need feedback so they develop bite inhibition, which means this is the stage in life they learn how hard they can and can't bite. With other dogs/puppies, if they bite too hard the other dog will either snap back or will stop playing with them. This teaches them that if they bite too hard, the play/fun/interaction stops. Eventually most dogs will develop a soft mouth (gentle, inhibited bite).
2. You have to allow them to bite gently but when they bite too hard, immediately stop the play or interaction. That means turn away, ignore them, etc.. If you turn away and the puppy keeps trying to bite, give the puppy a 30 second time out. Puppy bites too hard > put puppy in a room alone for 30 seconds. Repeat over and over as necessary. Some puppies learn right away, others take a few weeks or more. The key is you have to be 100% consistent so the puppy associates the hard bite with the end of the fun/interaction.
3. Never hit or smack the puppy. This can cause all kinds of psychological and behavior problems. Remember, this is normal puppy behavior and should not be punished using aversives or pain. It can be punished by taking away something the puppy wants - play/interaction/etc...
4. Puppies need to chew. Always have an acceptable chew toy available for the puppy. In some cases, if the puppy is biting you, you can try to redirect it to bite the chew toy. Puppy bites you > take your hand away and put the chew toy in the puppy's mouth. If the puppy ignores the toy and goes for your hand, 30 second time out.
5. You can do the same when the puppy bites the other puppy. If the other puppy doesn't provide feedback, then you can intervene and put the biting puppy in a 30 second timeout.