If the stain is Toning or Tarnish, leave it. It is considered part of the natural state of the coin and does not significantly effect the value unless it is REALLY ugly. If the stain is a substance that is ON the coin (ink, grime, oil, dirt, so on), you can often remove it by soaking the coin in soapy water. I would not rub, I would not do anything else. If the coin is circulated, you could use the tip of a rose thorn to try to work it off. The tip is soft enough that it will not scratch the metal, but could remove some of the grunge. Don't work it too hard.
When a coin is stuck, the metal expands into the design cut into the die. As that happens, small stress lines appear on the surface. These are the luster that new coins have. It is VERY light, very delicate. It can be removed by rubbing with talcum (it is that soft). Once that luster is gone, nothing can ever bring it back. Many coin dips use a light acid to remove the tarnish from a coin. It does this by removing the top layer of silver. It can take away the luster layer. If the coin is truly uncirculated, you can wash it, but I would not do anything else. Good luck.
