The VM, especially the 'gilded' version, doesn't wear well under any circumstances, becoming easily worn and scratched. Some medals have been lacquered. This can be easily taken off with nail polish remover. If you need to remove excessive dirt or fingerprints, just use simple soap and water and a toothbrush. If, however, you are of the school of thought that no self-respecting soldier would go on parade with dirty medals, then there are several products on the market which can be used for cleaning and polishing.
White spirit is a good de-greasant.
Try to avoid any abrasive metal polishes. Goddard's produce a product called 'Silver Dip', which is available in most supermarkets. The idea is that you dip the silver medal in the liquid, leave it for two minutes, then rinse in water. This leaves a clean but dull finish which can be buffed up later with a dry cloth. Doesn't work for bronze medals though, and is frowned upon by collectors.