First build a 2 zone charcoal fire (hot on one side, cool on the other). If you're using a gas grill, preheat your grill by turning half of your burners on medium-high to high and leave the other half off. The objective is to cook the dough quickly on the hot side, take it off, put on your toppings, and then place the topped pizza on the cool side to melt the cheese and warm the ingredients on the other of the grill using indirect heat.
Now I know what you're thinking... Doesn't the dough fall through the grates? Doesn't the dough stick to the grates? Nope, not even close - so set your fears aside and grill some pizza.
Get your dough ready spreading it to about a 1/4 inch thick. If you can go thinner by all means go for it, but be aware that the thinner the dough, the faster it will cook. I also like brushing it or spraying it with olive oil. Below is the raw dough just after being placed on the grill.
The cooking of the dough/crust goes fast - like, real fast - so DO NOT leave the grill, do not answer the phone, do not get a beer. OK if you're quick you can go get a beer, but walk fast! I would say that this dough (below) was turned after about 45 seconds. I told you it was fast.
I flip the crust probably 3 or 4 times. I want to cook the crust through but I don't want it to burn. By flipping it a few times I'm able to achieve that.
Pizza crust after flipping.
After the crust is cooked, remove it and add your toppings. Obviously the sky is the limit here, so add anything and everything you want! Now place the pizza back on the grill but this time put it on the cool side. Again, you want to warm the ingredients and melt the cheese. This process takes about 4-8 minutes depending on the heat of your fire. When your cheese is melted, you're done. Slice it up and enjoy!