Prepare your dough as directed in this recipe, or start out with a premade pizza dough.
Divide the dough into 4-6 dough balls. On an oiled surface, roll each with a rolling pin as thin as possible to make 10-12 inch circles. Then place a piece of parchment paper over the dough, letting it stick. Turn it over so that the parchment paper is underneath the dough, and brush the dough side with olive oil.
Preheat the grill to medium high heat, and have a hot and cold side on the grill. (I have a 3 burner gas grill, and I switch on just one side and the middle burner, and leave the last one off so that side of the grill is cooler). Clean and oil the grill grates.
Gently flip the pizza dough over the grill grates with the down side down, and peel off the parchment paper. Close the lid, and cook for 1-2 minutes. When the bottom of the pizza looks done, flip the pizza and cook for 1-2 more minutes.
Move the pizza dough over to the cool side of the grill and add your toppings (sauce, cheese, and any other desired toppings).
Lower the heat of the middle burner if needed. Close the grill and allow the cheese to melt.
Use grill tongs to remove the pizza from the grill and serve.