Soak the broiler tray for several minutes in hot, soapy water. Slip on latex gloves and then scrub the tray with the abrasive cleaning pad to remove loose and burnt-on bits. If the broiler isn't too dirty, this initial soaking and scrubbing might be enough to get it sufficiently clean.
Take the broiler tray to an outside area. Slip on latex gloves and then spray the tray with oven cleaner. Place the pan inside a black garbage bag, tie the bag shut, and let it sit for several hours. While it sits, the oven cleaner will break down the grease and burnt food.
Bring the broiler tray inside and rinse it off in a sink with hot water. Use the abrasive cleaning pad to scrub off any last pieces of grime. Wipe the broiler with a towel or let it air dry before replacing it in the oven or in a storage drawer.