In a large bowl of a stand mixer combine 1/2 cup of the warm water with the sugar and yeast. Stir to dissolve the yeast and let rest for 5 minutes.
Add the remaining 1 cup of warm water, and the olive oil, salt and vinegar.
Begin mixing on medium-low speed, gradually adding the flour, and knead the dough for about 7 minutes, or until it's smooth and elastic. The dough should be slightly sticky, but not so sticky that it really sticks to your fingertip when touched.
Cover the bowl with a dry towel and allow to rest in a warm place until doubled in volume--about 1 to 1 1/2 hours.
Gently punch the dough down and place on a lightly greased or floured counter top. Divide the dough into 2 or 3 equal pieces (depending on how thick you want your crust/how big you want your pizza. I make three medium size, thinner crust pizzas. But you could make two larger pizzas).
Roll and stretch your dough to desired size and thickness.
Allow the dough to rest while you preheat your oven to 450 degrees F. If you have a pizza stone (or want to use a baking tray) place it in the oven while it preheats.
Brush pizza dough lightly with olive oil and prick it all over with a fork. Pre-bake the dough on a hot pizza stone or in pizza pan for 6 minutes.
Remove from oven and add pizza sauce and toppings. Return to oven and bake for 8-15 more minutes or until the crust is golden and the cheese is bubbly.
Make ahead instructions: Option 1: Make the dough up until the first rise. Place the dough in an airtight container in the fridge to rise overnight, or for several hours, before rolling it out and pre-baking it. Option 2: Completely make the pizza dough, including pre-baking it in the oven for 6 minutes. Top with desired pizza toppings, cover well with plastic wrap and refrigerate for several hours, until ready to bake your pizza.To freeze the dough: Form a ball with the dough and lightly spray it on all sides. Wrap it in plastic wrap and place it in a ziplock freezer bag in the refrigerator for up to 3 months. To thaw, place the pizza dough in the refrigerator overnight and roll it out when you are ready to pre-bake.To freeze the pre-baked crust: Make sure the crust cools completely and then wrap it in plastic wrap and tinfoil and store it in your freezer. Only freeze pre-baked crust without the toppings!