If you find a gold coin that you want to sell, don't clean it. The dealer, collector or other buyer will probably want the coin uncleaned, and will pay more for a dull one than a shiny one. After all, buyers who prefer their coins clean know how to do it.
Of course, if you want to clean coins for your own collection, there are a few options open to you. The most obvious one – rubbing or using abrasives – is something you should avoid, however. Metal polishes put little scratches on the surface of the coin and remove little bits of gold. No one likes a polished, scratched coin. Be careful wiping your coins dry after cleaning, too. Gold is very soft, and even a cloth that looks gentle can leave little scratches. Dab coins dry after cleaning, or use an air blower, instead.
Dirty gold coins can be cleaned safely using gentle detergents or soap and a little water. Some people will use a little soap in a pan of water and boil the coins gently over a hot burner until they're clean. This is best for large lots. Never let the pan boil dry, however. Your beautiful gold coins will turn black! If you have access to an ultrasonic tank, you can use it to vibrate your coins in a cleaning solution and remove dirt, instead.
To take off stains, you'll have to think about what caused them. Many stains will come off with acetone (nail polish remover), which also takes off the residues from tape. If you use a solvent, be sure to do it in a well ventilated space. Once you've removed stains, you'll want to avoid sticking anything to your coins.
For rust stains, caused by coins that have been stored in contact with rusty iron or steel, use a weak acid. Soda, lemon juice and vinegar all work very well for this purpose. Rinse your coin afterward to get any sticky residue off. Persistent rust stains can be removed with more concentrated or stronger acids.
If you have a proof coin, with a highly polished surface, you need to be extra careful. Nearly any contact can cause problems with the beauty of these rare coins. You must avoid rubbing at all costs, and dry these coins extremely careful. Don't touch these coins with bare fingers, either. You'll leave a fingerprint that will spoil the shine. For most of us, gold proof coins are something that should be cleaned by professionals, as are many other gold coins. Think hard about whether yours need cleaning, and if they do, be careful!