I usually scrape what I can off with my pocketknife. What's left I either use coarse sandpaper, steel wool, or Comet. Of course I wear cotton gloves. No fingerprints on my shiny coins.
When I was working in a coin shop, a lady brings in a F/VF 1801 Bust Dollar as well as a few VF Bust Halves of various years....(I still cringe while writing this) all with mirror finishes... Oh it gets worse. When asked if she did this or if they had always been like that, she replied that she had just taken a silver cleaning cloth to them because they were grey and dingy and she wanted to make them look good before she brought them in.
brasso! It makes cents look like gold and silver look like platinum. Then cover the coin with Glo-Coat. It'll keep that look forever.
Excellent advice here for the newer collectors. May I just add for the benefit of such, please remember to always hold a coin by it's edges and turn your head to one side to avoid breathing on the surfaces.
I take beat up coins with "crud deposits on em" and soak em in vinegar or rub Taco-Bell Hotsauce on em .... but it makes them look fake and too shiny so then I hit em with a sand blaster that is filled with micro pebbles of titanium soaked in battery acid, dip them in flour and molasses, then wipe off the excess temporary gunk. After that, they look old again... then they just look like a beat up penny that hasn't been cleaned. :dead-horse: please... my reply is just sarcasm... but if you like your coins that way, and they are junk to begin with, I don't see a problem with cleaning em to fill a spot in a folder or something. In fact, I do have a cleaned set of the mid range wheaties that I salvaged at .04 each and put into a Whitman.
Wait!! Didn't you hear!!! Canada has made the first glow in the dark coin... the reverse is a dinosaur, when you turn off the lights, the bones in the dino glow.