Place a pizza stone in the oven if you have one. Preheat oven to 500 degrees F (or 475 if that's as high as your oven will go) while preparing the pizza dough so it can be completely hot when you are ready to bake the pizzas.
Combine warm water, sugar, and yeast in a large bowl. If using active dry yeast, let it proof for 5 minutes until foamy. If using instant yeast, there is no need to wait for the yeast to proof.
Add flour, olive oil, and salt and stir well with a wooden spoon or mix in a stand mixer with a dough hook until combined.
Knead for 5 minutes using a stand mixer fitted with a dough hook attachment or 6-7 minutes by hand until smooth and elastic. The dough will be tacky and slightly sticky, but should still be manageable to work with.
Drizzle a clean bowl with a little olive oil, then place the ball of dough in the bowl and turn it to coat in the oil. Cover with plastic wrap or a clean cloth and let rise for at least 30 minutes (or up to 1 ½ hours) until doubled in size.
Divide the dough into 2 or 3 balls (or more if you want to make personal-size pizzas).
Roll, pat, or stretch the dough out until it is roughly ¼" thick, then top with ¼-1/2 cup of pizza sauce, freshly grated mozzarella cheese, and other toppings.
Bake for 5-10 minutes until the cheese is melted and the crust is golden brown and crispy around the edges.
Cool slightly before cutting and serving.