In medium bowl, whisk together white rice flour, tapioca starch, baking powder, xanthan gum, and salt.
Using your hands, cut in the shortening. Do this by using a snapping-like motion with your fingers. No large pieces of shortening or lard should remain.
Add 1/2 cup cold water. Stir with a wooden spoon. Dough will be dry. Add another 1/4 cup water. Stir. Feel the dough. If it starts to hold together and feels damp, stop adding water. If the dough feels dry, add another two tablespoons water. Repeat until dough is moist but not wet.
Generously white rice flour your countertop. Turn dough out onto counter. Flour your hands lightly with white rice flour. Gather dough into a ball. Knead the dough until smooth. If the dough is too wet, knead additional white rice flour into it; if the dough feels dry, knead a splash more water into it. You want the dough to be easy to work with. Pull off a little. Roll it between your palms. It should not stick or fall apart. The dough's texture should be similar to clay or play-doh.
Cover dough with plastic wrap. This prevents a skin from forming.
Heat 10-inch cast iron skillet (non-stick pans don't work well. They don't get hot enough.) over medium heat. While skillet heats, line a tortilla press with a cut open plastic bag. (Only cut open the bag on two sides. The “hinge” of the bag should line up with the hinge of the press.) Dust the bag with white rice flour. Pinch off a dough ball, about two tablespoons. Roll dough into a ball.
Place the dough ball into the press and close to flatten. Slide the bag off the tortilla press. Gently pull the bag away from the tortilla. Lift the tortilla into your hand. Pull away the second piece of plastic. If the tortilla seems thick (which doesn't happen too often), dust the bag with flour, return the tortilla to the bag. Dust the top of the tortilla, cover, and roll out a little.
Increase the heat under the skillet to medium-high if the skillet isn't smoking lightly. Place the tortilla into the skillet. Cook, about three minutes, until the tortilla is golden brown.(As your first tortilla cooks, begin pressing out the next tortilla.) Flip. Cook an additional minute. Remove and place hot tortilla onto a plate. Cover with a clean, dry towel.
Repeat. Tortillas are best enjoyed right away. You can store them overnight in a sealed bag. Reheat by placing into a warm skillet.