I know little about fossils but I do know a little about photography.

Good lighting is very important especially with autofocus digital cameras. If you have poor light you get poor focus. I either shoot near a sunlit window or near several electric lights. You might get a color shift with electric light but you can compensate for it in programs like Photoshop. Another option is daylight balanced light bulbs. Some digital cameras have preset filters to compensate for indoor lighting. Another thing to watch out for is hard shadows. To get the best detail you want a well lit area with light from several directions.

I have noticed that fossil and mineral specimens photograph better with an opposite colored background. For example a light colored specimen will usually look better and show better detail shot against a black background. Likewise a dark specimen will usually look better against a white background.

Some specimens may require closeup or macro photography to capture the fine details. A tripod and remote trigger can be useful for these conditions and also helps reduce focus problems from camera movement when forced to shoot in low light conditions.

Another handy trick you can do in Photoshop is to duplicate the image layer so you have the same image on multiple layers. Then you can use the image filters to solarize 1 of the layers. Now you use the layer controls to manipulate how the filtered layers and original layers interact visually. This can reveal shapes and patterns that are hidden other wise. I often do this and also use another layer to invert the color and shade to add to the mix.

That's a few simple things I know. I hope it helps someone!