Like many Americans who cook Mexican food, I always thought that tortillas came in a package of 10, soft and flexible when fresh, hard and brittle when they quickly turn stale. When we were in college (way long ago), La Super-Rica Taqueria opened and introduced us to what real Mexican street food was like. Instead of commercial tortillas covered in cheese and guacamole they served (and still do) simple fillings in tortillas that were cooked just before in went into your mouth.
The basis of tortillas is Masa, a Mexican dough. Making masa is actually a fairly complicated process of first making hominy, which is then cooked and ground. It is then sold as dry masa harina (to which you add water) or as a lumps of wet dough. These lumps may be in different consistencies depending on if you are planning to make tortillas, tamales or, pupusas.
Once you have your lump of masa, you cut off a piece of about a quarter cup and roll it into a ball. At this point you can flatten it by hand, by patting it into a circle. However the easier technique is to get a tortilla press. This is a device that has two plates the fold over on one another and a handle that presses the top plate sown on the other. To make a tortillas: 1) you flatten the ball of dough slightly,2) place the dough on the bottom plate, 3) fold the top plate over the dough, 4) fold the handle over the top plate, and 5) press down on the handle. When you open the press the dough has been squished into the flat disc you are familiar with as a tortilla.