I don't think "inexpensive" and "photomicroscopy" are ever uttered in the same sentence. That said, there are some things you can do.
What kind of microscope do you have? Binocular? Trinocular? The easiest thing is if you have a trinocular 'scope, of course. There you have the extra eyetube just for the camera. But, there are adapters made to take the place of one of the eyepieces in a binocular or monocular 'scope, too. In those cases it's just not as easy for you to see what's going on while you're taking photos.
Then it's just a matter of getting adapters to mate camera and scope together. What kind of camera do you have? I have a DSLR. I managed to find an adapter that would take trinocular port to a T-mount. From there, there are T-mount adapters to fit most SLRs.
I had an extra computer sitting around and my DSLR came with software that enables the computer to control the shutter release. That really helps to keep the whole setup from shaking while taking the photograph.
So, if you have any more specific questions, I'll be happy to try to answer them for you.
Good luck!