Don't say besides not smoking, stop smoking! It will help a LOT. My mom had to stay in the hospital for 4 days because she could not breath, all because of smoking. It scared the crap out of me. She quit a few months ago completely, and shes getting healthier and healthier every day.
The best way to get rid of nicotine stains on fingers is by soaking the affected fingers in a solution of lemon juice and warm water. You should repeat the step often until the fingers are amply cleansed.