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Stains result when any foreign agent- be it ink, rust or chocolate pudding- land on a porous surface. (A 'porous surface' is a surface that has microscopic pits or holes that can't be seen with the naked eye.) When these pits or holes fill with ink, the object of the game is to get it back out before it has time to settle in- that's why it's important to attack a stain while it is fresh. The longer a stain sits, the harder it is to get it out.
With ink, you'll want to use a cottonball (or soft rag) dipped in rubbing alcohol. However, take extreme care to test for colorfastness first! The problem that comes with getting any stain out of any surface is the increased potential for damaging the finish of a stained surface.
If you are not particularly concerned about the finish, try the rubbing alcohol and see if the stain will come out that way. If it does not- or if you are concerned about hurting the surface, then it is time for a new coat of paint!