Mineral photography is just a great application of what folks call "macro photography" in the photo world. The typical approach to this is the use of macro lenses and extension tubes or bellows (although macro lenses are not strictly required). Whole books have been written on macro or closeup photography (I particularly like the ones by John Shaw).
The mineral macro photographer has many things working in his favor. In particular his subjects are not crawling around, or being blown about in the wind. There is plenty of time to arrange and rearrange lighting, and with a digital camera it is possible to just experiment and try again and again.
It is possible to do mineral photography through a microscope in several ways (for example, I have a microscope with a third tube, intended for the attachment of a camera). I intend to try this out and compare the results I get with those from lens and bellows setups. I have heard several people say that this is not the road to go down. Some people attach a camera to a microscope eyepiece (a method known as eyepiece projection) and get acceptable, but not excellent results.
Here are some essays I have written on related topics:
Tom's Mineralogy Info / email@example.com