Is your camera a DSLR or is the lens part of the camera? Does your scope have a photo tube or will you be attaching the camera to an eyepiece?
Attaching a DSLR is much cheaper than a point and shoot. My photo tube is threaded at the end. All I had to do to attach my Nikon body (a film camera) was buy a C-mount adapter ring. Point and shoots require specially designed adaptors which insert into a phototube or an eyepiece tube. Cost of these adaptors is expensive, up to US $300-400. The eyepiece adaptor for my Sony F717 was $350; a second piece designed for the phototube was $100. They take focal length down the eyepiece tube into consideration and some of them have their own lenses. Martin Microscope <www.martinmicroscope.com> makes adaptors for Nikons, Sonys, and one Canon. They have supplemental information and an image gallery which are useful for beginners.
Some non-DSLR have small diameter lenses which can be just held next to the scope eyepiece. You can get some surprisingly good pictures this way. The down side is that there might be vignetting or worse, scratches on one lens or the other. For these it's best to have them on a tripod or copy stand & positioned a few milimeters off the lens. Use black paper & roll it into a tube which extends over both the lens & the eyepiece to eliminate extra light leaking in; tape or rubber band both ends. Which reminds me - whenever you attach a camera to one eyepiece always cover the other eyepiece with cloth or a tube when you're ready to click the shutter. If not you may get images of overhead lighting leaking through the other eyepiece. Took me a while to figure that the strange rectangular blur in my first attempts was the ceiling fluorescent!
As I said TTL doesn't work on a microscope (or telescope, thanks Joe). Your strobes will not be controlled by the internal exposure meter. You can get excellent shots using normal microscope lights instead of strobes by allowing the internal meter to determine exposure as long as there's no external sources of vibration. These shots will be long - up to several seconds depending on the light source. A bouncy floor, a nearby door closing, an overhead fan moving the seawater, someone walking by or sharing the work table - these will all cause vibration and blur the image. Some colleagues of mine have work tables made of concrete, wood, & tile - no nasty vibration there! I always get great shots using these.
Use the microscope for magnification not your camera. If your camera has digital zoom don't use it. Scope images at high resolution become pixellated anyway; using the digital zoom just increases the pixellation. Use the camera's regular zoom just enough to eliminate any vignetting in the image (although this is unavoidable with some cameras).
My favorite web sites on macro- and microphotograpy are <www.macrophotography.com> and <
http://www.microscopy-uk.org.uk/>. You'll find lots of great information as well as stunning images.