I've had good results using a little laundry detergent mixed in with water. I basically dip a rag in the water/detergent solution and ring it out real well. Then I gently wipe down the grill cloth until it is damp. I then use a soft toothbrush to lightly scrub the grill cloth. Then I dry it with a dry rag. Whenever possible, I use this same method to clean both sides of the grill cloth. The grill cloth has always looked great afterwards.
p.s. don't use a "ratty" rag or paper towel (unless you blot it), as it will shred and then you'll have to pick out the shredded pieces from the grill cloth, which is not fun, trust me :x
