Sorry I have taken so long to respond here, but this is how I make pita bread. Super simple. You'll need:
1 cup warm water
1 tsp. sugar
2 1/2 tsp. (1 pkg) yeast
1 cup rye flour
2 1/2 cups bread flour (more or less)
2 tsp. olive oil
1 tbsp. sea salt or kosher salt
Mix 1 cup warm water with 1 tsp. sugar and 2 1/2 tsp. yeast (or 1 package). Stir together and let rest at room temperature for about 15 minutes, until bubbly.
Stir in 1 cup rye flour, whisk well, and let stand for another 15 minutes or so, to hydrate the flour.
Add 2 tsp. olive oil, 1 tbsp. sea or kosher salt, and 1 cup of bread flour (all purpose flour will work, but not nearly as well, since rye is low-gluten). Mix vigorously -- I use the paddle attachment on my stand mixer and just beat the daylights out of it for about 10 minutes, then switch to a dough hook for another 8-10 minutes. You want to work up as much gluten as you can. The dough will be sort of sticky and shaggy.
Spread about 1/2 cup flour on a work surface and turn the dough out onto it. Knead it gently into a ball shape, working in a little of the flour if necessary so it just holds together and is nice and soft. Oil your mixing bowl well, roll the dough ball around in it to coat, then cover and set aside to rise for 1-2 hours. The longer you wait, the better -- but once it is doubled in volume, you can consider it done.
Punch down the dough gently, then divide into six or eight pieces, depending on how large you want your pitas to be. Roll them into balls, then cover again and let rise a second time for at least 30 minutes.
Meanwhile, put a cast iron skillet or pizza stone in the oven and heat it up to 450°F. You want it REALLY hot.
When the balls of dough have "poofed up" a bit, you can start rolling them out into circles, about 1/4" thick. You might need a little more flour to make sure they don't stick to the work surface as you turn them.
One the pitas are shaped, be sure to cover them so they don't dry out. Once they've been rolled, try to let them rest for another 15 minutes before you actually start to cook them.
To cook, place them one at a time on the preheated skillet or pizza stone and close the over door. If your oven has a window in it, you can watch them puff up and form the pocket in the middle... if not, wait 3 minutes and DON'T PEEK BEFORE THEN! Once they have puffed up, let them brown slightly, another 30 seconds or so, then remove from the oven and cover with a kitchen towel while you cook the rest of them.
To make pockets, just slice the rounds in half and open them gently with a butter knife or your fingers.
These will store just fine for several days in an airtight bag, but be sure not to put them in there until they are completely cool or the condensation will make them soggy!!