1. Make sure you have enough fuel.
Gas grills: Empty propane tanks can be quite embarassing. If your grill doesn't have a built in scale to indicate when you need propane, try one of these gauges.
Gas grills: Heating on high for ~ 20 minutes will burn food off of grates making them easier to clean with a brass brush.
Charcoal grills: Check that bag; it's probably not as full as you last remember. If you are planning on grill for a long time (> 1 hour), use charcoal that does not have lighter fluid already on it (ie Matchlight). Adding this to hot coals will catch fire quickly and possibly send someone to the hospital.
2. Preheat the grill and clean cooking grates.
Charcoal grills: Once coals are ashed over, place cooking grate and lid on and wait about 10 minutes before brushing grates.
3. Cook at the right temperature using the right method.
Direct Heat For foods cooking for less than 30 minutes. Steaks, burgers, vegetables
Gas grill: Using a four burner grill as an example, all four burners would be on for direct heat.
Charcoal grill: Coals arranged in one layer filling grill.
Indirect heat For foods cooking longer than 30 minutes. Typically larger meats.
Gas grill: Only the first and fourth burners would be lit.
Charcoal grill: Coals on each side of grill leaving space in middle for drip pan.
Seafood Direct high heat
Burgers & Steaks Direct medium heat
Boneless Chicken breast Direct medium heat
Bone-in Chicken Indirect medium heat
Ribs Indirect low heat
Vegetable Direct medium to high heat
4. Right tool for the right job
Brass cleaning brush
Long handled spatula
Large set of tongs
Silicone basting brush
Oven mits with long sleeves
I hope these tips help you out. Now get out there and grill!