Caveman style of cooking is where you take something like chicken and throw it in the fire, leave it sit for a little while and then pull it out and pick all the black stuff off it. While that is effective it doesn't always taste that great. This instructable is about a better method that gives results that you can be comfortable sharing with someone else.
Step 1: Chicken Prep
My preferred type of chicken for BBQ'ing is chicken thighs. The reason is that thighs are a dark meat and so tend to not get as dry as white meat does. They also have a fair amount of fat which helps to produce the smoke that makes it taste really good.
I buy a bulk package which is usually enough for a full kettle.
Unpack your chicken and put it in a big bowl. Add some BBQ sauce as you add the chicken pieces and stir it so all the pieces are coated. Do NOT remove the skin, the skin keeps the thighs from burning when they are first put on the grill.
For the sauce I use any regular BBQ sauce, something like one from Kraft or Hunts. It takes about half the bottle.
THIS is the most IMPORTANT step. Take the whole bowl after you have mixed in the sauce and put it on the rack in your oven. If you forget this step, when you come back from lighting your kettle you will find a very happy cat on the table, a large mess and not as much chicken as there was when you left.