Perhaps the most important step that most people don't do is allowing the steaks to sit once they are taken off of the grill. The steaks need to rest for 5 to 10 minutes before serving or cutting them. This gives the juices a chance to redistribute throughout the steak, which both helps it finish cooking evenly and keeps the meat moister and more flavorful. Place the cooked steaks on a cutting board or platter and tent loosely with aluminum foil. Once rested, either slice or serve the steaks whole.
When the grill is cool, remove the grates and flavorizer bars and put them into a full bucket of soapy water. Let them soak for at least 15 minutes. Remove anything else from the grill that you can take off without tools, like burner control knobs and the grease tray. This will make it easier to clean. Most gas grill burner tubes are removable as well (look for simple cotter pins on one end, although some models use screws).
Clean the bottom of the grill with a soapy sponge. Once all the chunks are gone, scrub the bottom with a sponge or scouring pad and soapy water to remove any built up grease or grime. Lots of drippings and food scraps tend to build up under the burners of the grill. Pay close attention to this area and clean it as much as possible to avoid corrosion.