Use a long-handled scraper to remove any hard, baked-on food from previous use
Remove cooking grids and spray with a good degreaser. Maybe even use an oven cleaner on them!
Hose down the grill, inside and out, and if it's in need of painting, use a paint that can handle high temperatures, so it won't peel off after using the grill a few times.
To prevent any unexpected dangerous tip-overs, make sure the grill wheels are tight and secure.
For propane grills, carefully check the hoses for cracks, and make sure all tubes are clear.
Replace any lava rocks or corroded grates. Check that there's sufficient propane in your tank and test the burners.
It's wise to refer to your grill's manual and keep it handy for specific needs
