Warm ½ cup of water to 100°F (roughly 30 seconds in the microwave). Stir in sugar until it dissolves. Then sprinkle yeast over the top of water. Allow to bloom for 5 minutes.
Add 1 cup of flour to a small bowl and pour in the yeast mixture. Stir to combine until no dry spots remain. It should be very loose. Cover and rest for 1 hour. This is your starter.
In the bowl of a stand mixer, add remaining ½ cup of flour, olive oil, and salt to the rested starter.
Attach the bread hook, and knead on low until everything is combined. Then, turn the speed up to medium high and let it go for 15 minutes.
When the dough is done, it should be tacky but comes cleanly away from the bowl. You should be able to press a finger into the dough and have the print bounce back.
Form the dough into a ball with a tight smooth surface. Place into an oiled bowl.
Cover with a tea towel and refrigerate for at least 6 hours or up to 2 days. If you're making the pizza dough for tonight, do not refrigerate and allow to rise on the counter at room temperature until doubled in size (at least 2 hours).
To Make Pizza
Place a pizza stone onto the bottom rack of your oven, and preheat to 550°F (or as high as your oven will go) for half an hour.
Sprinkle cornmeal on a pizza peel and set aside. Cornmeal will act like ball bearings so your pizza will slide easily from the peel to the stone.
Flour your counter and press the dough out into a round of 14 inch diameter. Optionally, use a rolling pin to get the dough even. It should be fairly thin.
Move the dough to the pizza peel testing to make sure it does not stick.
Top your pizza with sauce, cheese, and toppings. Jiggle the peel occasionally to make sure that the dough is not sticking.
Once topped, immediately move pizza from the peel to the stone (see video in notes for how to do this).
Bake pizza for about 8 minutes or until cheese is brown and crust is cooked and bubbly.
Notes
Here's a video on getting your pizza off the peel and onto the pizza stone in your oven.