To mix the dough in a food processor: In the bowl of a food processor fitted with a dough blade or regular metal blade, combine the flour, yeast, salt, and sugar. Pulse a few times to mix everything together, then pour in the water and olive oil. Process until the dough comes together in a ball, then keep processing for 15 to 20 seconds.
To mix the dough by hand: Measure the flour, yeast, salt, and sugar into a large bowl. Stir the dry ingredients with a wooden spoon or dough whisk, then pour in the water and oil and mix until the dough comes together and all of the flour is incorporated.
Scrape the dough onto a floured countertop. If you mixed your dough by hand, flour your hands and knead the dough for about 7 minutes, until it forms a smooth ball that slowly springs back when you poke it gently with your finger. If you mixed your dough in a food processor, flip it until it's coated in flour, then knead it a few times, just until you've got a smooth, slightly tacky ball that doesn't stick to your hands.
Divide the dough into 2 or 3 equal-size pieces. (If you're making 12- to 14-inch pizzas, divide the dough in half; if you're making smaller pieces, divide the dough into 3 pieces.) Shape each piece of dough into a smooth ball, and place each ball in a separate airtight container. Refrigerate for 24 to 72 hours.
Take the dough out of the refrigerator about 2 hours before you plan to bake your pizza. (For best results, let your dough come fully to room temperature before you stretch or roll it out.) If you only plan to make one pizza, freeze the remaining ball(s) of dough for up to 3 months (click here for more on freezing pizza dough).
Preheat the oven to 500°F (if using a baking sheet) or as high as it will go (if using a baking stone/steel; place the stone/steel in the bottom third of the oven before you start preheating). Let the oven preheat for at least 30 minutes, preferably more like 1 hour. Then, if you’re using a baking stone or steel, switch the oven to Broil on high.
Roll or stretch out the dough to your preferred size. If you're working with a large ball, you'll get the best New York style results if you stretch or roll it out to a 14-inch round; if you're working with a smaller ball, aim for a 10-inch round. Pick the dough all over with the tines of a fork to prevent bubbles from forming in the oven.
Top your dough with your favorite sauce, cheese, and toppings. Transfer to the oven and bake until the crust is evenly browned and the cheese has browned in spots—8 to 10 minutes on the baking sheet, 6 to 8 minutes on the baking stone/steel.