Nicotine is a toxin. It is found in tobacco, a nightshade plant (as are tomatoes and peppers). Nicotine is an oily substance that combines easily with water and penetrates the skin. Smokers who smoke inside will find the substance also creates a yellowish film on drapes, walls, windows and the like. This staining can be difficult to remove.
Cut and open one lemon. Squeeze the juice from the lemon into a small bowl or cup. Rub some of the pith (the white part) of the lemon rind on the affected spot. Be certain that you have no cuts, abrasions or open sores on either hand, or else it's going to sting.
Take some of the juice (less than a teaspoon) into the palm of your hand and place a little salt in it, enough for it to feel gritty. Use this gritty juice to rub the stain out of your skin. If the salt is not effective, use a pumice stone or non-metal scrub pad.
Crush a plain (not coated) aspirin in warm water, if you do not have a lemon, or if you have a cut on your hand. Aspirin contains acetylsalicylic acid and will also be able to get the stain off your fingers. Run the crushed aspirin and water mixture into the stain and use a scrub pad or pumice stone to further abrade the stain if necessary.
Rinse your hands well after either treatment and apply again. It may take several tries before these treatments are successful. Be sure to apply a good moisturizer after scrubbing your fingers, as they will be very dry.
Apply cuticle remover to the stain if the more natural methods do not work. Cuticle remover is a harsher solution, but can help dissolve the stain and callousing caused by nicotine. Read the label before trying this solution; it may be too strong for your hands.