Puppies use each other as chew toys, so when they move away from their littermates and start hanging out with humans, it is only natural that they should continue their mouthy ways. Trouble is, we humans have skin that is so very delicate. In fact, it breaks when our puppies chew on it, and that is no good for anybody.
There are many suggestions for stopping puppy mouthing, and only some work for each puppy. My favorite, which I consider the standard technique for stopping puppy mouthing, is the startle and redirect method. This strategy consists of making a high-pitched sound that is best written as “AWRP!” This sound startles most puppies enough to make them release their hold on you. Then, you redirect your puppy’s mouth to something appropriate to chew on, such as a chew toy or other toy. Many people are really good about remembering to startle but then forget to redirect their puppy to something that can be chewed. The result of this mistake is that the puppy goes back to mouthing the person’s hands or clothing and the person thinks the technique doesn’t work.
There are other effective ways of dealing with puppy mouthing, but I advise against any aversive methods, even if they are commonly advised. For example, don’t hold the puppy’s mouth shut or stick your fingers in it, yell, or use physical force to stop the dog. Basically, anything that frightens or hurts the dog is not an option.