Here are some nice pictures and animations that show how a rotary engine works.

The rotary engine is a very simple device, with something like 3 moving parts on the inside (aside from the water and oil pumps and the distributer...etc.) Most of you know how a piston engine works. Well the fact is that those engine's, though powerful, waste a lot of there power towards friction. In a rotary there are no pistons, rods, crankshaft, cam, lifters, pushrods, valves, valvesprings...the list goes on and on. On a rotary there is the eccentric shaft, 2 rotors, oil pump, and distributer. Theirs some more crap in there, but those are the only things that are really moving in there. One example of a piston engine working against friction, is the fact that a slightly pumped up (ie heavier valve springs for a bigger cam) V8 engine  (16 valve) uses 30hp compressing valve springs! Hey, thats a free 30hp for the rotary.  Now think of a 16 valve Honda or a 32 valve Northstar...you get the picture. Thats just the valve springs, not to mention the cam, lifters, rockers, and all that other stuff. I'm not really knocking on other engines, I'm just saying that the rotary looks to be a way more efficiant engine.
This one shows basically how this thing works. The blue arrows are the intake, that is then compressed where the spark plugs are and the air/gas mixture is fired, the red arrows are the exhaust. The stationary gear meshes with the gear on the inside of the rotor. (not shown on the animation to the left)
This shows the parts invoved with the Wankel type motor. The red area is the rotor housing, the yellow part is the rotor, and the light blue is the eccentric shaft. The dark blue area is actually a stationary gear that does not turn, it keeps the rotor in the right position at all times.
This is an animation that is using actual parts.
What is a Rotary? Wankel Engine?
More Rotary Animations for you to enjoy