Some of my fingers on my left hand have gone completely numb. At first, they just tingled. Who should I see for this?

Start with your PCP. Without more information, it is difficult to assess who would be best in evaluating the symptoms of numbness. Some options include a neurologist or orthopedic surgeon. Consider starting with your family doctor or internist first. He or she can do some preliminary tests and make the appropriate referral, if necessary.
Primary Care. With most things, you can really approach your family/internal medicine doctor. They know the right questions to ask to either treat you or send you to the correct specialist. In your case, it would be good to know more information or perhaps run certain tests before sending you for referral.