Certain practices can help discourage deposits of dirt and grease from forming in the first place. One method is to grease the grates of your hot grill with a little cooking oil right before your start cooking. In the same vein, scrubbing your grill grates with a raw onion is another tactic you can try. If you do have a grill brush without bristles, it's a good idea to scrape your hot grates both before and after grilling.
Clean the exterior of the grill. Soapy water is the safest cleaning solution for most gas grills. Just make a cleaning solution with water and a squirt or two of mild dishwashing soap. Wipe the exterior of the grill with the soapy water, use a rag dipped in clean water to remove the soap residue, and then dry the exterior of the grill thoroughly.