It is not generally advisable to clean gold coins on your own.  Like all expensive things, it is best left to a professional who knows his job.  If you damage the gold coins while cleaning it, you may damage it and the value too.  However, if you are keen to undertake this task yourself, given below are some tips to do this properly.

Some things to avoid:

1. Do not clean your gold coins with chemicals and cleaners that are abrasive.  Gold is a very soft metal and it can be scratched very easily.  Even a soft cloth can leave scratches on gold.
2. Do not wipe your gold coins dry.  Like explained above wiping them after cleaning can leave tiny scratches.  You should pat them dry or use a hair dryer to dry them.

The Right Way to clean your gold coins

Experts advise you to clean your gold coins by soaking them in warm soapy water.  Use the mildest dish washing liquid you can.  Check that the ingredients are not too harsh.  Use warm water and just one teaspoon full of dish washing soap to one pint water.  If possible use distilled water.  Tap water also contains chemicals.  Use a plastic tub or bucket to clean your gold coins in.  After a few moments, take the gold coins out and dry them on a towel already placed for the purpose.  Place the gold coins far away from each other since even the edges touching could leave scratches on the surface.

Experts have special equipment to clean the coins.  Most of them use ultrasonic tanks.  Sound waves create a vibration in the soapy water contained in the tank.  This creates ripples in the water that gently remove the grime from the surface of the coins.
Removing Stains

There are many kinds of stains that can tarnish the surface of your gold coins.  Generally stains can be dissolved using the simple homely nail polish remover.  If the stains are caused by rust, you can use lemon juice or vinegar.
However, this being said and done, it would be wiser to let the experts handle something as valuable and precious as gold coins.  Even a small act of negligence could leave scratches that will lower the value of the coin.