Puppies nip for all sorts of reasons.
We need to be intelligent in how we deal with it, so that these baby animals are properly understood and of course, learn human rules.
A puppy naturally uses their mouth for many things, which is why leaving them in a crate to 'punish' the mouthing makes very little difference. Isolating him might allow him to calm down, but other than that he will go back to a very natural, normal nippy puppy.
Saying 'No' is also meaningless and is likely to scare the puppy and make him bark at you in fear. What we can do, however, is train and properly redirect him depending on what he is nipping for, who, and when!
Firstly, is he over-excited? A puppy likes to jaw wrestle in play, so in these situations it is best to give your pup something chewy and tasty. A Kong toy with a scrape of something inside such as meat paste rather than an edible chew is best. This will attract his mouth to this item rather than hands. If he needs to calm down, it is time for bed, along with the chew toy.
Another common reason is simple over-tiredness. Puppies get tired very quickly, and they nip harder. Nap time! (with his chew of course).
Manners must be taught, by you, and gently does it. Puppies play with anything that moves or smells interesting, so clothing and hands are prime targets. If this becomes tricky, provide puppy with an alternative toy to grab. If he grabs hands or clothing, stop moving and stop play. Offer the alternative toy, and praise him for this. These games are best played with an adult at first. Kids find it very hard to stop leaping and squeaking which of course, pups love. They treat them like other puppies! So, the rules of play have to be taught by sensible grown-ups.
Rough play makes mouthing considerably worse, and teaches puppy to use physical force. That family member who says it doesn't matter, that they can handle it, that you are being 'soft'? They will leave you with a pulling, pounding puppy that as he grows will only become more physical. If you must play like this, keep it feather-light.