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An almost complete tortilla writeup

There are really two kinds of tortilla: one is Spanish tortilla, and the other is Mexican Tortilla.

Spanish Tortilla

To these Italian eyes, it looks like a frittata. It is made with fried potatoes and fried onions, mixed with egg, and fried in a pan. It is fried on one side until it sets, and then very carefully flipped so that the top side gets nice and golden.
Very common in Spain. Every Spaniard is convinced that his mother makes the one and only tortilla, and that everything else sucks.

Mexican Tortilla

There are two major varieties, made with corn and wheat flour.

The wheat flour tortilla (in Mexico tortilla de harina) is made with wheat flour, fat and salt. It is very thin and flexible. Typical of Northern Mexican cookery, it crossed the border and ended up in burritos.

The corn tortillas are made with hominy ground with water. The result dough traditionally was flattened and cooked on a comal, although nowadays there are machines where the dough goes in from the top, and finished tortilla come out from the front: you normally find them in Mexican tortillerias.
Notice that the corn is usually the most common yellow variety, but blue, red and brown corn can also be used, resulting in colorful tortillas.
People claim that the taste is different.
Tortillas must be eaten hot. You can reheat them on a comal, in a pan without fat, in a microwave oven (keep them wrapped in plastic, or they will dry up), or even on an open flame. Yep, that's right: just plonk one on the gas burner and keep it there for a half minute.

Hot tortillas are usually served wrapped in a cloth, to preserve the heat: notice that a cold tortilla is not very flexible, which prevents the forming of tacos.
Tortillas are eaten at the table, but they also form the base for some recipes, like sopa de tortilla, chilaquiles and torta azteca.

Update: the wily anthropod gives you the right way to make corn tortillas. All hail anthropod! I have made themselves that way many times while living in the tortilla-less parched wastelands of Paris and Pittsburgh.
And in fact, many tortillerias here in Mexico make them in this way, by rehydrating masa harina (as opposed to the molino de nixtamal places, that make their own hominy and grind it and generally have a more difficult life).
If you have forgotten your trusty tortilla press somewhere, a useful trick is to squeeze the dough ball between a pot and a countertop - of course, using the fundamental plastic sheet trick.