Dissolve yeast in 1/2 cup of warm water. Add the sugar and stir until dissolved. Let sit for 10 to15 minutes until water is frothy.
Combine flour and salt in a large bowl. Make a small depression in the middle of the flour and pour yeast water mixture into it.
Slowly add 1 cup of warm water, and stir with wooden spoon or rubber spatula until elastic.
Place dough on a floured surface and knead for 10 to 15 minutes. When the dough is no longer sticky and is smooth and elastic, it is done.
Coat a large bowl with vegetable oil and place dough into the bowl. Turn dough upside down so all of the dough is coated. Allow to sit in a warm place for about 3 hours, or until it has doubled in size.
Once doubled, roll out in a rope, and pinch off 10 to 12 small pieces, just smaller than a tennis ball. Place balls on floured surface. Let sit covered with a towel for 10 minutes.
Heat oven to 500 F and make sure rack is at the very bottom of the oven, and heat the your baking sheet as well.
Roll out each ball of dough with a rolling pin into circles. Each should be about 5 to 6 inches across and 1/4 inch thick.
Bake each circle for 4 minutes until the bread puffs up. Turn over and bake for 2 more minutes.
Remove each pita with a spatula from the baking sheet and place on a wire rack.
While still warm, take a spatula and gently push down on each puff. When they are thoroughly cool, place in storage bags.
Pita bread can be stored for up to 1 week in a pantry or bread box or up to a month in the freezer.