In a bowl, mix yeast and sugar into one cup of water, warmed to skin temperature (not hot!) in the microwave oven. Stir well and allow the yeast to come alive for five minutes.
Mixer method: Combine the flour, olive oil, and salt in the bowl of a mixer fitted with the dough hook. Add the water with the dissolved yeast and mix on the second-slowest speed until the dough pulls away from the sides of the mixer bowl. If necessary, add a little more water at a time to get a very smooth, but not sticky, dough.
Place the dough on an oiled baking sheet or pizza pan. Cover it with a damp, clean towel, and let it rise for an hour and a half in a warm, moist place. (The inside of an oven, turned on for one minute then turned off, works well.)
When the dough is double its original size, punch it down and divide it into six balls. Flatten these slightly, sprinkle with flour, and place them on a pan, well apart. Let them rise again for about 30 minutes.
Fire up the grill to get a medium-high heat. Roll out the dough to about 10-inch diameter. Do not make a lip at the edge. Place the dough right above the fire. Let it bake for one to two minutes, until lightly browned on the bottom. (It may balloon; this is okay.)
Turn the crust over and top with the sauce, cheese, and other toppings. Let the pizza bake above the fire until the cheese has melted and the sauce is bubbling--three to five minutes. You do not need to close the top of the grill. Remove from the grill with a large spatula or a pizza peel. Slice and serve immediately.