Aluminum foil might not be the first tool that comes to mind when you're about to clean your grill, but it probably should be. You can use foil to easily scrub down your grill. It also has the added benefit of helping remove any rust. All you need to do is turn on your grill and set the heat to high in order to loosen up and burn off any grease or large chunks of debris. Then, ball up a piece of foil and get to scrubbing.
You might want to make sure you use a pair of gloves when cleaning, but the foil should easily get rid of any leftover debris. The abrasive foil will work much better than a brush or sponge.