Inside Surfaces
Clear ashes from the bottom of the kettle after each use once the ashes are cool. Do not allow ashes to remain in the kettle. The ashes can absorb moisture, and may cause premature rusting of the cleaning system. Brush the carbonized grease from the inside of the lid. Wash the inside of bowls and lids with warm soapy water and rinse.
Grates
After the coals have died out, brush off any loose particles on the warm (not hot) cooking grate with a brass grill brush. Wash with warm soapy water, then rinse. A soapy scrub pad will remove any stains.
Ash Catchers/Pans
Empty after each use once ashes are cool. Do not allow ashes to remain in the ash catcher. The ashes can absorb moisture, and may cause premature rusting of parts.
Gas Grills
Brush the Burner Tubes
This one is big, because it's the key to maintaining even heat across your burners. Using an up-and-down motion, clean any debris off of the burner tubes, using a stainless steel brush. Do not brush lengthwise across the ports, as this will only push debris from one hole to another.
When finished, light the grill and check for even distribution.
Clean the Cooking Grates
Preheating the grill and burning off residue by turning the grill on "high" will turn any accumulated debris to ashes. Brush the grates off with a brass grill brush.
Clean the Flavorizer Bars
You really don't ever need to remove the Flavorizer Bars from your grill to clean them, since preheating the grill and burning off residue by turning the grill on "high" is enough to turn any accumulated debris to ashes. Occasionally brushing the bars off with a brass grill brush should be sufficient maintenance.
Clean the warming racks and control panel
A soapy, fine steel wool pad will keep the warming racks clean and free of smoke stains and debris. It will also remove grease spots and stains from a porcelain control panel, but use a very light touch so as to not scratch the porcelain. Rinse thoroughly. If the control panel is stainless steel, use a cleaner formulated for stainless steel. Always clean in the direction of the grain. Do not use abrasive pads, as they will scratch.
Clean the outside of the endcaps and cookbox
You should clean up grease drippings on these exterior surfaces as soon as possible. Grease can be damaging to painted surfaces. Use mild, soapy water and rinse thoroughly. Harsh or lemon-based cleaners can ruin the paint finish on the endcaps and cookbox.
Stainless Steel Surfaces
Use a cleaner formulated for stainless steel. Always clean in the direction of the grain. Do not use abrasive pads, as they will scratch.
Clean the Bottom Tray
Use a plastic or Teflon® scraper to remove excess grease. Wash with warm soapy water and rinse. Do not line the bottom tray with foil. The bottom tray should be cleaned after each grill use.
And if you haven't done it lately...
change the catch pan liner underneath your grill.