First things first: Carefully consider the location of your grill: It should not be near anything combustible, the house, overhangs, walls, trees, or shrubs. It should never be indoors.
Now comes the cleaning part (courtesy of a Charmed Wife's Lily Fink Harrington):
1. If you have a gas grill, spread a layer of aluminum foil over your grill and turn it on. Close it and let it "cook" for 30 minutes or so. Turn it off, carefully remove the foil, let it cool, and then use a wadded up piece of foil to scrub the grates. (Like the "self-clean" option on your oven, all of the gunk will have turned to ash and will flake right off.) Skip this step if you have a charcoal grill.
2. Wait until the grill is completely cool. Remove the grate, then use a scrub brush and warm soapy water to scrub it clean. Set the grate aside and allow it to dry. In the meantime, remove whatever components are under your grate and scrub them clean, as well, sprinkling baking soda on any tough areas. Dispose of any charred, caked bits and ash.
3. Replace the grill parts. Then, using the same soapy water and baking soda (Bar Keeper's Friend works well, too), clean the dust from the outside of the grill using a sponge. Finish up by cleaning all the plastic parts and knobs with Mr. Clean's Magic Eraser. It'll look like new.
Some safety tips to keep in mind before you fire her up:
* Always be prepared for flare-ups. Have a fire extinguisher at the ready for emergencies and a box of salt or baking soda handy for smaller flare-ups.
* If you are using a gas grill with a propane tank, make sure the tank is level and always turned off when not in use. Before use, while the grill is still cold, check it for leaks by opening the valve and rubbing or spraying the hoses and connections with soapy water. If the soap bubbles, you have a leak. Never try to repair a tank valve or a grill yourself; see a qualified repair person.