Preheat grill to medium-high heat with the lid shut. While the grill is heating, make your dough (recipe below) and get all of your toppings ready. You need to have everything ready to go when you start cooking the dough, because it goes fast once you start. It's easiest if you put all of your toppings on a platter next to the grill. Roll out your dough with a rolling pin and brush (or spray) one side of it with olive oil. Place that side down on the grill and shut the lid immediately. It will probably take 5 minutes or less to cook that side, but make sure to leave the lid shut for most of that time, so the grill will cook the dough all the way through. If the dough is cooking too fast and hot, move the pizza off the direct heat. You want nice brown grill marks, without burning it.
Before you flip it, brush (or spray) a little olive oil on the other side. As soon as you flip it, quickly add the toppings and shut the lid. The bottom side will cook really fast, so if the toppings are not warmed/melted, but the crust is cooked, move it to the top rack away from direct heat, and close the lid until done.
You don't need as many toppings when grilling as normal pizza because the grill gives it such a great flavor, you don't want to overpower it with toppings.
Pizza Dough
5 1/4 cups unbleached flour
1/4 cup sugar
1 1/2 tsp. salt
1 Tblsp. + 1 1/2 tsp. SAF instant yeast
1 Tblsp. + 1 1/2 tsp. liquid lecithin
2 cups hot tap water
Mix in electric mixer for 1 minute. Check for dough consistency. Add water if needed. Knead for 5 more minutes in mixer. Do NOT add more flour. Cut into desired amount of pieces for how many pizzas you want to make. Roll into desired shape. Cook. This recipe will make two medium sized pizza or several personal pizzas.