Add the yeast and water to a bowl and stir with a wooden spoon. Allow the yeast to dissolve until it is incorporated into the water, about 5 minutes. Add the olive oil, salt and 1 1/2 cups of the flour. Stir the mixture with a spoon until until the dough forms a ball, or place all the ingredients in a food processor until the dough forms a ball. After a few seconds of mixing or processing, add the remaining 1 1/2 cups flour. The dough should be soft but not sticky. If it is too sticky, add a bit more flour and process for another minute.
Transfer dough to a lightly floured work surface and knead dough for 2 to 3 minutes, adding enough additional flour if necessary to form a smooth and elastic dough. Dough should not be sticky. Transfer dough to a lightly oiled 2 or 3 quart bowl and turn to coat dough with oil. Cover with a damp towel and let rise in a warm place until doubled in size, usually at least 1 hour.
Preheat oven to 500 degrees F and if you have one, place a pizza stone on the bottom rack of the oven.
Divide dough into 2 portions (for 2 (12-inch) pizzas) and form into balls. (See note below for calzones.) Place on a lightly oiled baking sheet and cover with a damp towel. Let rest for 15 minutes, then transfer to a lightly floured surface, shape as desired and roll out to a thickness of 1/2-inch. Transfer dough to a pizza peel and top with toppings of choice. Transfer to the preheated pizza stone and bake until crispy and golden brown, usually 12 to 18 minutes (depending on the toppings). Remove from the oven with a metal peel or spatula and serve immediately.
Note: For calzones, divide the dough into 4 equal portions and form into 4 balls. Place on a lightly oiled baking sheet and cover with a damp towel. Let rest for 15 minutes, then transfer to a lightly floured surface and roll out into 4 6-inch circles. Place filling of choice in the center of one side of each circle, then fold dough over filling to meet edges of filled side. Crimp edges with a fork or your fingers, then cut a small slit in the top of the calzone to allow steam to escape while cooking. Cook on a preheated pizza stone in a preheated 475 degree oven for about 8 to 10 minutes, or until well-browned. Remove from the oven with a metal peel or spatula and serve immediately.