Using your hands, spread the pizza dough to form a 1/4-inch thick pizza. Brush one side with olive oil and put it, oil side down, onto the grill. Brush some more oil on the top and close the cover. Cook until the bottom is browned and the top is set, about 5 minutes. Flip the crust over and cook on the other side until browned, about another 3 minutes. Remove from the heat and set aside until your guests arrive.
Spread some tomato sauce onto the crust and top with mozzarella and your favorite toppings. Put the pizza back on the hot grill, close the cover, and cook until the cheese is melted and bubbling, about 5 to 6 minutes.