This is the real Greek pita. I found this on a Greek web site. I think it was Susie's Place. This can be used for souvlaki and gyros sndwiches. If you bake this longer, you have pita pockets. The time to make includes rising.
Add 1/2 cup of the warm water and let it stand for 10 minutes to proof and ferment.
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 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 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 oven to 350 degrees.
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" thickness.
Set 2 or 3 pitas on a lightly oiled cookie sheet and bake them on the lower rack 2-3 minutes each side.
Bake longer for pita pockets.
Susie's note: 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 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.