If you spend a little time watching a litter of puppies playing, you’ll notice they bite each other as part of their play. While this might look cute when they’re young, their puppy teeth, also known (for good reason) as needle teeth can hurt pretty bad, and even cause welts and cuts. When you're bleeding, the cute puppy love bites are no longer fun.
It’s our job to teach our puppies that biting people is not acceptable behavior. It's our job to show our puppies an alternative behavior that satisfies the puppies drives to bite or to correct the behavior. There are a number of ways to do this. Which method you choose is up to you.
When litter mates play with one another and one gets bitten too hard, it yelps. This yelping is their way to communicate that the play is too rough. So, there are times a human using a sharp, loud sound is enough to teach the pup that what they are doing is over the top. If the puppy stops biting, then you can praise it with a calm "good boy/girl" and a treat or a toy to play with. Using too excited of a voice to praise your puppy may cause them to go back into prey drive and you'll be right back at square one. How you say things to a puppy is often more important that what you're actually saying.
You can also use the method of redirection. If your puppy tries to play roughly, simply toss a soft toy a couple of feet away. It'll teach him that biting you is boring and chasing toys or playing tug is much more interesting because you bring the toy to life. To perfect this method, you must also teach the puppy to out. Toys that you use for reward are soft and not safe to leave with the puppy all the time. They're only for reward, not a possession of theirs and therefore, they must return possession to you on command.
With small puppies, one of the worst things in the world that can happen to them is for them to have to be still. They absolutely hate it. If your puppy bites you, simply hold him still on his back. He will likely protest and struggle but hold him still until he calms down. If you're consistent with this method, he'll associate him biting you with him being restrained. He'll stop to avoid being put in "timeout." That said, never use the crate as punishment if you crate train.
Correcting puppies is another method that is more old school, but still works. This method is dated, but it still has value if your puppy bites really hard or is older and causing damage to yourself or kids and you need to curb the behavior quickly. A lot of trainers back in the day would say simply grab the offending pup by the scruff and shake until they whined. Today, you might go to jail for doing that! A better method is to keep your puppy tethered when it's not in a pen or crate. That way, you have access to give a leash correction at all times.
The key to all training is consistency. Some puppies like to bite relentlessly. You have to be just as relentless in your consistency and hold steadfast. Allowing your puppy to get away with the behavior sometimes is sending mixed signals and will result in poor results and an extended learning curve.