Nipping and biting are common problems with the majority of dog breeds, including Yorkshire Terriers (which are often referred to simply as "Yorkies"). Yorkies tend to bite when they are young puppies and are still adapting to and learning about their environments, although older dogs occasionally bite as well. It is important to stop your Yorkie from biting as soon as possible to avoid escalation of the issue (and also to prevent them from biting and potentially harming someone else).
Limit physical and energetic play time. If a Yorkie has been allowed to bite and feels that he has a position of power within the house, he will keep participating in the same behavior as he grows older. Quit engaging in physical games with your Yorkie, at least temporarily. Make a concerted effort to avoid dominance-related activities, such as challenge games (tug-of-war, wrestling and chasing).
Set boundaries. It is vital your Yorkie does not feel like she is the boss of your house. Specify certain areas in the house are that strictly "off limits" for your Yorkie, and follow through in making her respect these boundaries. You can do this by repetitively removing her from these areas and telling her "No." Maintain a dominant body posture and look your dog in the eye as you discipline.
Encourage licking as opposed to biting. This technique is particularly effective for Yorkie puppies. When a Yorkie licks your hands and arms, gently praise him to indicate that you prefer this behavior over the biting. Encourage licking by providing your Yorkie with a little incentive to do so. Rub a dab of butter over your fingertips to reinforce this behavior.
Discipline your Yorkie. When your dog bites your hand or fingers, speak in a authoritative voice and command him with words such as "No biting" or "Bad dog." Look directly into your Yorkie's eyes as you do these things, and maintain your posture for several moments. Stay calm as you are doing this. After those moments are up, go back to your normal behavior and demeanor.
Discourage your Yorkie from biting by "retaliating." Put a little bit of bitter apple spray over your hands, so when your Yorkie bites you, he is dissuaded by the unpleasant taste. After several repeated efforts to bite you and tasting the spray, he will likely stop biting.