In a large mixing bowl (or right in the bowl of a stand mixer, if you like), stir together the flour, yeast, salt, and sugar.
Pour in the water and mix well (by hand or with a wooden spoon or silicone spatula) until all the flour is hydrated.
Pour in olive oil and mix until incorporated.
Knead dough for 10 minutes. I like to use a stand mixer fitted with the dough hook, but you can do it by hand if you like.
Divide dough into two equal pieces and form each piece into a ball. Lightly oil and place into two separate sealed containers. Lidded glass food storage bowls or quart-sizes takeout containers works well.
Let dough rise in the fridge for at least 24 hours, up to 72 hours.
An hour before you you want to bake the pizzas, remove dough from refrigerator. Set a pizza stone or steel on a rack in the center of the oven and preheat oven to 500°F (260°C) or higher if your oven goes higher.
When ready to bake, remove dough from container. If you're a newer pizza maker and would like the extra security of a less sticky dough, feel free to flour it generously.
Stretch the dough into a rough 14-inch round. You do not need to do a perfect job to end up with good pizza.
Top the pizza judiciously. For cheese pizza, I use a not-obscene amount of thick tomato sauce, grated pecorino cheese, and low-moisture whole-milk mozzarella that I shred right before topping.
Slide the pizza into the oven and bake for 10 minutes, until cheese is melted and bubbly and crust is cooked and browned in spots.