Using hardwood charcoal, build a split fire. Put 1/2 the coals on each side of the grill and leave an open space between. (If your charcoal grill is too small to do a split fire you can try the same method with one hot side and one cool side.) Place the grate over the fire and allow it to heat up for 5 minutes. Use a grill brush to clean the grate. Hold a paper towel dipped in vegetable oil with long grill tongs and oil the grate.
Slide the dough onto the grate between the two sides of the fire. Poke it all over with a fork to pop the bubbles that will form as soon as the dough hits the heat.
After a minute or two the edges of the dough closest to the fire should no longer be raw. Use two large spatulas to spin the dough a quarter turn so that the two sides closest to the coals are away from the heat and the other two sides are now facing the coals. Lift the dough occasionally to make sure no spots are burning.
After about 4-5 minutes the bottom of the dough should be baked and just lightly browned. The top of the dough should be pale but set and probably bubbling. Use a fork to pop any very large bubbles.
Brush the dough with olive oil and then add the toppings. Keep an eye on the bottom of the dough and continue to spin quarter turns to avoid burnt spots (personally, I like a little char). Sometimes I'll move the pie over one of the hot spots very briefly to evenly brown the bottom of the crust.
You can remove the pizza from the grill and finish baking it in the oven if the bottom of the crust is done baking before the toppings are ready. I usually preheat the oven so I can finish baking the first pizza while I put the second pizza on the grill.