Set the shutter speed to the slowest value you can without getting much motion blur from your hands shaking - this will take some experimenting on your own. Then set the ISO pretty high and hope for the best!
If you have a canon, set the dial to "P" (I think most dslrs have this) mode and move in close to the screen so your camera can detect more light and have a faster shutter speed reducing shake and what not =).
The problem (at least with Space Mountain) is that with the monitors have a certain amount of "flicker." If your shutter speed is too fast, you'll end up with part of the monitor being dark. I usually use a shutter speed of around 1/50th of a second for this; it seems to eliminate the flicker, but my hands are steady enough to still get a clear image with my 24mm lens.