"What a cute puppy!" everyone says to you; while you are thinking, "I am about to go nuts with the puppy biting and chewing!" Puppies using their teeth is as natural as humans using their hands. Think about it. Dogs don't have hands with opposable thumbs, they have teeth and they use their teeth for everything. Teaching puppies to use their teeth appropriately is the task at hand -- NOT elimination of using their teeth.
There are many great books out there you can refer to -- I like Ian Dunbar, Patricia McConnell, Jean Donaldson, Morgan Specter, Andrea Arden, Melissa Alexander, Karen Pryor -- any book written by a positive reinforcement trainer is going to supply you with a wealth of good information. Check them out and pick one that fits with you and your puppy. The great thing about books is that it is a readily available source in a moment of "aaack! what do I do?!?" and they remind us that we are not the only humans with puppies that need to be taught!
What to do about those pointy, sharp puppy teeth? Make sure puppy has appropriate things to chew on. Puppy-proof the space puppy spends time in. Never leave puppy unattended to chew indiscriminately (and to potty, get into trouble, and generally wreak havoc!). When puppy bites/nips the humans in your house, act completely offended and ignore the puppy -- hands away (pockets, armpits, crossed over your chest), stand up straight, look away from the puppy, and stand completely still -- for just a minute or so (puppies have short attention spans, so this time doesn't and shouldn't need to be very long). If it hurts when puppy bites (as opposed to being just completely annoying), yelp "ouch!" like puppy's canine siblings or playmates would do in addition to ignoring puppy. When puppy is playing nice with you, be sure to give her lots of positive reinforcement. Rewarded behavior is repeated behavior and ignored behavior is behavior that goes away.
If you have other pets and are trying to teach your puppy to fit into your existing family, the above statements still apply, but there is an added component -- the other animals. My first strategy is to supervise their time together, but allow the animals to work it out amongst themselves. When and if you need to intervene, we like a long, braided, fleece tug toy to distract puppy, These toys have a lot of "life" in them when we move them around -- and that's what is attracting puppy to the other animals in your family. When the toy comes to life, puppy is enthralled and distracted from pestering the other animals. Ta, da! Puppy is positively reinforced for leaving the other animals and interacting with the toy!
Find a positive reinforcement clicker training puppy class that includes puppy playtime/socialization and enroll. So many people put off this very important component because they think puppy is too young (we enroll puppies as young as 6 weeks with their vet's approval and encourage puppies to enroll before they are 12 weeks old), or puppy is doing fine at home -- we don't need any help, or because they don't know/understand how important socialization is. Puppy class is not necessarily about obedience, but more about being with other people and puppies. The obedience is just a great bonus! In our puppy classes we spend time on house manners, attention/focus, and coming when called; the end of each class is puppy playtime where the puppies are let loose to play and interact with each other. We strongly believe that puppies learn a wealth of information from each other and older dogs that cannot be learned from humans. So we encourage lots of interaction.
When puppy class is over, keep teaching and working with your puppy. Puppies turn into teenagers and I think the teenaged time is much more trying than puppy time. I encourage all of my puppy students to continue coming to some kind of class through the teenaged time -- it helps keep your teenaged pup on track as well as supporting you during this interesting, exciting, and trying time in your young dog's life.
And last, please don't wish your puppy time away -- they are puppies for such a short time. Yes, it's crazy, sometimes messy, but always a joy and it's gone in a blink. Enjoy the puppy breath, the puppy sounds, the puppy faces -- build your relationship and enjoy the beginning of a long and happy journey with your puppy.