To start with, the single best way to look after your medals and awards is to have them handled only by professionals. A professional medal mounter handles precious medals day in day out, and knows what works, what doesn't, and how to deal with any problems that may arise without causing any further damage.
At the end of the day, if you leave your medals in the hands of a 'hobby' or 'part time' medal mounter, don't expect a professional job, and don't whine about the result, you get exactly what you pay for!
OK, lectures out of the way! Here is how we recommend you look after your medals. Some may disagree, but these methods work.