Depending on the type of ink, you might try oil-based hand cleaners such as Goop or acitrus-based solvent, or an alcohol-based solvent, such as isopropyl rubbing alcohol. Though it's very hard on the hands and can damage clothing, dilute bleach works for ink-jet stains.
You can try using some removing it using certain alcoholic products such as alcohol wipes, nail polish remover, paint thinner. However stronger product such as the pain thinner is not as recommended. Nail polish remover or the alcohol wipes are the best choice though if you have.
A product called Amodex is a favorite among fountain pen users and it works on a variety of inks. It was invented in the 1950s by a printer and was specifically designed for safe use on skin (its base is lanolin).
For use on fabrics, though, one of the Carbona "Stain Devil" spot treatments may be cheaper. There are nine different formulations and the directions differ subtly, so sure to read carefully.
Stain Devil #3 is the one optimized for inks.