Puppies bite. This is not a form of aggression, but a form of play and communication. It's important to train a puppy not to bite in play or to communicate, as this behavior can become unacceptable and even dangerous in an adult dog. This is a very important lesson for a puppy to learn.
For many puppies, all it takes is the owner "Yiping" when puppy teeth touch human skin for them to stop this behavior. Give a "Yipe!" and stop the game for about 15 minutes after you've had to yipe to get pup to take teeth off you. That's what another puppy would do, and it helps the puppy understand.
This sound needs to be what a puppy would do when the idea is "Ouch! That hurts! I don't like it! Stop it right now!"
In the litter, that offended puppy would then retaliate in some way, or refuse to play with the rough puppy for awhile. Some puppies have strong predatory instincts that are overstimulated when a person yipes, and for these puppies this would then not be an appropriate method.
Also, make sure no one is playing "mouth games" with the puppy, encouraging it to put teeth on humans for any reason. You need to react with your "yipe" or other intervention every time teeth touch a human, whether it hurts or not, so the puppy will understand this vital concept: no teeth on people. Even a gentle touch could get someone hurt if they jerk their hand away, and people will do that, especially kids.
My favorite intervention for a dog putting teeth on people in play is not a quick fix, but it has nice benefits and is very safe to do with most dogs. I simply hold the mouth closed for 15 seconds (work up to this time--at first it might frighten the dog to hold for more than about 5 seconds), while praising the dog. I say "[Dog's name], Close Your Mouth. GOOD Close Your Mouth!"
This teaches the dog the words for the behavior I want--and eventually you can remind the dog about the mouth by just saying those words. But that stage won't last long, because if you are very consistent about doing this intervention every time the puppy puts teeth on people, eventually the puppy will never do so at all.
By handling the mouthing from a positive point of view with praise--although it's still a correction: done every time the dog mouths a person's skin, it shows the dog the correct behavior of keeping teeth off people and praises the dog for doing it--you gain other benefits, such as accustoming your dog to being comfortable having someone control its mouth.
You do have to be consistent and stay with this over a period of time to get really solid results. Dogs not taught about teeth on people do not automatically outgrow it, so this is time very well spent training your dog. This method works on adult dogs as well as puppies, and is much safer for both you and the dog than harsh corrections.
Teaching a dog never to put teeth on humans is for family dogs. For some types of work dogs might do, the trainer may not want to create this strong inhibition against putting teeth on human skin. In those cases, the trainer may manage the puppy mouthing behavior by simply putting a toy in the dog's mouth. We can definitely take a cue from these trainers by redirecting our dogs' mouthing behavior into their toys, after we have carefully shown the dog not to mouthe us.
I also find it useful to teach the dog the word "Kiss" for licking. When the dog is highly stimulated in play and seems to need to touch me in some manner, I can remind the dog "Kiss" and then praise the dog for licking me.
In the early stages of working on mouthing behavior with a puppy or new dog, keep in mind that you want to teach any new behavior/command in a quiet situation with minimal distractions. So start teaching "Close Your Mouth" with the praise at times when the dog is quiet. Soon you can do it quickly and smoothly whenever mouthing occurs, even if the dog is excited. But you will in the process be bringing the dog's excitement level down and helping your dog develop self-control.
The praise is important to helping the puppy or dog learn to have no fear of a human taking control of its mouth. You are praising the puppy for accepting the restraint at that instant, not for the mouthing done 3 seconds ago.
And be sure you don't cause your dog to bite its lips or tongue when you restrain the mouth--it should be comfortable for the dog, as it should be any time you require your dog to obey any command of yours.