The word "quesadilla" roughly translates to "little cheesy pastry" in Mexican Spanish, and it's a fairly apt description, although instead of true pastry, a corn or flour tortilla is commonly used — flour in northern Mexico, corn most other places. In some versions, the quesadilla is made with a raw tortilla whose edges are crimped together around the filling before cooking, which results in something a little more like a turnover. Along with burritos, enchiladas, tacos, taquitos, and tamales, quesadillas have become a staple of Tex-Mex cuisine, their popularity fueled by the ease and economy of their preparation as well as their versatility. The possibilities with quesadillas are nearly limitless — from completely vegetarian versions to hearty, fusion-inspired creations. Fill it with anything from chicken to buffalo, have it with beans or no beans, but most importantly, don't forget the cheese.
Despite all the variations, though, every quesadilla starts out pretty much the same way. Take a skillet large enough to fit a tortilla (preferably nonstick, for ease of release) or preheat a grill. Cook the fillings, set them aside, wipe down the pan or grill, lightly oil the surface, and then add a tortilla. Heat it through quickly, then add the cheeses and other fillings to one half of the tortilla and fold the other half over it. Press it down with a spatula so that the cheese sticks to the tortilla. Carefully flip the quesadilla and brown it lightly on the other side. As an alternative, use two tortillas, spreading the cheese and other fillings over the whole bottom layer, then topping it with another one and proceeding as above; in Mexico this is called a sincronizada.
That's pretty much it. Cut the quesadilla into wedges, serve with a dollop of sour cream, garnish with some cilantro, and enjoy with some nice, hot salsa and a margarita.