Scrape first with aluminum. As soon as you are done grilling, before you've even turned your grill off, ball up a piece of aluminum foil and scrape the grill, going up and down following the grill bars. Do this until you have completely covered the entire grill. This will remove the biggest pieces of food and debris.
Reheat the grill. Cover the entire grill top with a very large piece of aluminum foil. Close the lid to the grill and turn the heat up. Let the grill stay at this high heat for at least 10 minutes.
Use the steel brush. After 10 minutes or so, turn the grill off, open the grill and remove the aluminum foil. The more stubborn bits of debris will have loosened a bit. Run the brush up and down the grill bars, the way you did with the aluminum foil. This time, however, apply more pressure. Go over the grill twice to get all of the debris.
Wipe down the grill for small debris. Soak an old dishcloth in a light cooking oil. Using tongs, rub the cloth up and down across the grill bars. This will pick up any remaining small debris that might be left after scraping the grill with the brush. It will also leave a coating of cooking oil of the grill bars for future use that will help keep food from sticking in the future, thereby making your grill cleaner and easier to use.