If your fingers become a moving target each time you go to pet and greet your puppy, don't take it personal. Instead, try to understand why your pet companion has a finger-nibbling fetish and learn how to correctly nip his nipping behavior in the bud.
Nibbling at your fingers can be your puppy's way of testing his boundaries to see whether you'll establish yourself as the leader or whether he'll have to become the leader. When you bring your puppy home, you become his pack. Before this time, his litter mates formed his pack and he would use his mouth to establish his rank. To raise a well-mannered, obedient puppy, put a stop to his nipping to send the message that you are in charge.
If your puppy is nibbling at your fingers and every other object in sight, the teething process might be to blame. Just like young children, all puppies go through a period where they lose their puppy teeth so the adult teeth can come in. This causes discomfort in your puppy's mouth. Chewing, nipping and biting eases the discomfort. Provide your pet companion with plenty of chew toys and frozen wet washcloths to nibble on so he leaves your hands alone.
Neglecting to exercise your puppy can result in his nibbling behavior. Exploring, chasing your hands and putting his mouth on your fingers is fun to him and might be his way of burning pent-up energy. Rather than feeding into your pet companion's excitement by vigorously petting him, pet him gently with slow strokes and increase his daily exercise. A game of fetch is ideal, because it burns energy and teaches him acceptable items to put his mouth on.
To stop your puppy's nibbling, arm yourself with dog treats or toys each time you reach for him. Feed him the treats or show him a toy while you pet him so he associates your greeting with pleasant consequences. If he nips at your hand, stop all activity, look him in the eye and yelp "Ouch" as if you're in excruciating pain. After he calms down, continue petting him, and again, stop all the fun as soon as he starts nipping. With consistency, he'll stop going after your fingers to avoid putting a damper on the attention he's getting.