In a mixing bowl fitted with a dough hook, place flour, yeast, salt and sugar. While mixer is running, gradually add water and knead on low speed until dough is firm and smooth, about 10 minutes.
Turn machine off. Pour oil down inside of bowl. Turn on low once more for 15 seconds to coat inside of bowl and all surfaces of dough with the oil. Cover bowl with plastic wrap. Let dough rise in warm spot until doubled in bulk, about 2 hours.
Preheat oven to 500 degrees F.
If using a pizza stone, place stone in oven on bottom rack, preheat oven 1 hour ahead. Punch dough down, cut in half. Place half of the dough on generously floured work surface. By hand, form dough loosely into a ball and stretch into a circle. Using a floured rolling pin, roll dough into large circle until very thin. Don't worry if your circle isn't perfect and if you get a hole just pinch the edges back together.
To prevent dough from sticking to counter, turn over the dough and sprinkle with flour. Also, flour the counter top and rolling pin as needed. Sprinkle pizza peel or cookie sheet generously with cornmeal. Transfer dough to pizza peel or cookie sheet with no lip. Add toppings. Slide dough onto pizza stone or place cookie sheet with pizza on bottom rack.
Bake 10 to 12 minutes or until golden. Roll out remaining dough and top with desired toppings or freeze in freezer bags.