Gomers bike is what it looks like after youve truely ridin in MUD.:p I wish I had a picture of the time my brother and I went for a ride on the clay road by our house when we had 2 inches of rain and still raining. Clay sticks to everything, and we had so much clay on our motorcycles, the front tire would not move at all! It was packed full of clay, it looked like a big clay donut. You couldnt even tell what kind of bike it was. I seriously bet we had at least 50lbs of mud and clay on our bikes.
I go with my quad buddies all the time. Mud is a LOT easier to ride in than clay BTW. Gomer and Psyco Diver have explained it well, the only thing I can add is KEEP YOUR SPEED UP!!! This is the single best thing you can do in the mud. The faster you go, the cleaner your tires are, the cleaner the tires are, the more traction you get. Keep the back tire clean so you dont slide so much.