Photomacrography.net, linked above, is the place to go to learn all about the options, equipment, and techniques involved.
Note that newer microscope objectives are infinity-corrected, requiring a converging lens (AKA "tube lens") to produce good results. The converging lens can be an ordinary camera lens. Objectives come in a bewildering array of specifications, and most types are not particularly well suited to being used directly attached to a camera.
Older microscope objectives can indeed be used on a bellows.
In either case, once magnifications go above 5x or so, DOF is so shallow that large image stacks are needed to deal with most subjects. So you need a very stable rig with fine control of camera and/or subject movements.
For up to 4x you can get good results with a reversed lens. There are very few lenses that allow you to go beyond 4x to good effect, because of the problem of diffraction. As Phil has recommended elsewhere, the K28/3.5 is outstanding reversed. It is sharp just one click down from f/3.5, and the shorter FL allows high magnifications with moderate amounts of extension.
I have a 10x rig, using a 10x objective (infinity-corrected) on a 200mm converging lens (DA*200). Or I'll put the objective on a 150mm lens (M75-150) for 7.5x, as here:
This is the eye-spot from the wing of a Luna Moth, stack of 85 shots.