Cut the pita bread into triangles (or, if larger, you may want to cut into strips/squares instead). You can leave the pieces joined around the edge or separate into thinner chips, as you prefer.
Place the pita bread pieces on a baking sheet then drizzle over the olive oil. Try to drizzle relatively evenly. Then, sprinkle over the za'atar (or other seasoning if you prefer, see above).
Toss the pita gently to coat them with the oil and seasoning - try not to bread them up too much. If some are not as evenly covered, you can rub them in the oil.seasoning that will likely be on the baking sheet to help coat them.
Place in the oven and bake for approximately 10 - 15 minutes. The timing will depend on how thick and dried out the bread is - if you split them, the thinner sides will cook quicker so check after eg 8 minutes. If the bread is fresh rather than slightly stale, they can take longer, sometimes nearer 20 minutes. Remove the chips once they are crisp and gently brown, and return any that are not ready yet to the oven.
Video
Notes
I used homemade za'atar spice blend which is really easy to make, but you can also buy ready-made. You can change the seasonings to suit as well, eg some salt, pepper, garlic and paprika.