Nipping and biting are a normal part of interaction among pack members in the world of the wild dog, coyote, or wolf. These are natural ways in which dominance is established and puppies are disciplined by their mothers. In the human world, however, these same behaviors are completely unacceptable.
Dogs who nip or bite can cause lawsuits, earn you legal fines, and even be taken from their homes and killed by Animal Control. Also of concern is the pain and suffering of the individual who is injured and possibly scarred for life . In the human world, the dog owner (a legal term) is responsible for the behavior of their dog. Therefore, it is to everyone's benefit, including the dog's, to make sure your dog knows what behaviors are acceptable and considered "good manners" by the human standard.
This is why taking your new dog, whether a puppy or an adopted adult, to basic obedience class can be an essential part of building a relationship between the two of you. Even if you think you know how to train a dog, training techniques continue to evolve. There are always new ways to handle situations, and some techniques that work well with one individual personality are a disaster with another. Even if you have taken your older dogs to school and now have a new puppy, there can be the added benefit of building a stronger bond between you and your puppy by going to class together. Each dog has a unique background and will interact with you as an individual.
Please understand that I am not a dog trainer and have nothing to personally gain by recommending dog school for you and your dog. I make this recommendation because undoing a problem is much harder than never allowing it to develop in the first place. That having been said, it is important to understand the many reasons why dogs bite. Aside from the fact that this is a natural way of communicating among dogs, there are other reasons why your dog might be exhibiting this behavior and why you may have a problem eliminating it.