My grill cleaning method has always been to put a layer of tinfoil on the grill, shiny side down. Ten minutes or so of direct heat and the grill is clean, just like a self-cleaning oven. If there's any ash left, a quick pass with a wet paper towel takes care of it.
I learned this the hard way. Cheap aluminum foil falls apart really easily at the kind of heats you would want to use for baking or grilling. It's worth it to even buy the Reynolds extra strength stuff. Worst part of grilling is if your tin foil gets holes in it, and now you've screwed up the moisture barrier.
