What’s cute in a little puppy is not cute, dangerous and hard to fix in an adult dog. On the whole, puppies don’t outgrow bad habits unless they’re taught that they are bad habits. A major reason why a lot of young dogs end up in shelters is because owners didn’t realise that puppies need training and attention, so the dogs get to a year or so old, mostly their adult size, but with little or no training. Not the dog’s fault.
There are lots of ways of fixing this, but what worked for me was that the minute I felt teeth, I’d stop the game and say, “no biting”. Nipping meant the immediate withdrawal of attention and fun, just stop and ignore the dog. If my pup kept going I’d hold his mouth and repeat, “no biting”. He was, and is, a very independent-minded dog, and it took a lot of repititions, but he got the point eventually. For really nippy puppies the key is to be absolutely persistent and consistent, once you’ve made the rule you have to keep it.
And teach the pup to sit, so that the sit is absolutely reliable…one sit and that little bottom hits the ground. I found that getting a good, reliable sit could circumvent any number of problems. A puppy at three months has a short attention span, but is perfectly capable of being trained.
Although puppies do need to learn self-control, they are still puppies with lots of energy, so rather than letting them get irritating asking you to play, volunteer. Throw a ball, or give them a toy they can chew on without doing damage, or give them a little training session, something short and simple for them to think about.
I’ve had this guy recommended to me: http://www.siriuspup.com/ and one of his books has a whole section on teaching bite inhibition to puppies.
I also liked “The Other End of the Leash” by Patricia McConnell a lot, a very sensible book with a lot of intelligent training tips.