Combine the yeast and sugar in a small bowl, add 1/2 cup of the warm water and let it stand for 10 minutes to proof and ferment it.
Dissolve the salt in the remaining warm water.
Put the flour in a large mixing bowl, making a well in the middle and put the dissolved yeast and salt water into it.
With your hands, blend it into a dough.
You may need a bit more or less water depending on your flour.
Knead the dough in the bowl with your fists for 10-15 minutes or until it is smooth.
Pour the oil over the dough and knead it again until the oil is absorbed.
Cover the dough in the bowl with a towel and set it in a draft free area to rise to double it's bulk (1-2 hours), then punch it down and knead it again for a few minutes.
Preheat your oven to 350°F.
Cut pieces of dough, egg size or larger, depending on the size of the pita desired, shape them into balls with your hands and roll them out over a lightly floured board or pastry cloth to 1/4 inch thickness.
Set 2 or 3 pites on a lightly oiled cookies sheet and bake them on the lower rack 2 to 3 minutes each side.
Pitas should be white and soft.
Wrap the baked pitas in a clean towel until they are cool, then store them in plastic bags to prevent them from drying out.
When you are ready to use them, heat a bit of oil in a shallow skillet and fry them a minute or so on each side, or until golden brown.
Use them immediately, because they get hard when they dry out.