When young dogs gnaw and nip fingers, often the tendency is to excuse it as "puppy behavior." But consider it "unacceptable behavior" -- behavior that will continue, and worsen, if you don't correct it.
Like a young child, a dog will test the limits to see if he can get his way, and to ultimately see who's boss. So you must set the limits.
Here are some techniques to try with your young dog. (But remember, each dog is an individual, and the root cause of a behavioral problem varies between individual dogs.)
* If your dog tries to nip during play, state "no bite" in a firm voice and stop playing. If he has his leash on, use it to give a correction if he doesn't obey immediately. Turn his eyes to meet yours; this will emphasize the point. As soon as he calms down, say "good boy." Giving your puppy or dog something to chew on instead of your hand is a good alternative technique.
* To teach a dog to allow you to take items from his mouth: Set him up for a correction. Put on his training collar (leash attached) before a play session. Give him a favorite toy or bone. Then, with the leash in your left hand (keep the training collar loose), command such "drop it" -- and immediately take the item from his mouth, then praise him with "good boy!" or "good drop!" If he locks eyes or bares teeth (don't wait for a nip), yank the training collar for an immediate correction, then release. If he drops the item on his own, praise him enthusiastically. The goal is for your dog to happily obey without any show of aggression.
If your dog shows any type of aggression, or you'd like to learn how to "child-proof" your animal, be sure to consult a professional trainer.