First make your filling. We like chicken but shredded pork is really good too. Chicken thigh meat is the best flavored. Cook it in a skillet or crock pot with some broth, chiles, tomatillos maybe, pretty much whatever flavors you like. If you want to do vegetarian, black beans and corn or plain cheddar cheese are good.
Then take a giant stack of corn tortillas. Fill a skillet with at least an inch of cooking oil and put it on medium. We use olive oil or grapeseed oil for health reasons. Grapeseed oil is fantastic for frying. If you heat olive oil hot enough for frying it loses the olive flavor but is still healthy.
Get a plate ready with some paper towels on it. Drop the tortillas in the oil 2 at a time. The oil should make tiny bubbles underneath the tortillas. After 30 secs to a minute or so, pull them out and drain as much oil off as you can, then toss them on the plate and put in the next tortillas. They should be really limp and wobbly. You need to do a lot of them and it takes a while but this is what makes them taste good. You can toss more paper towels on the pile to soak up extra oil periodically if you want.
Don't leave the tortillas in too long or they'll get crispy. If you accidentally do this you can use them for tostadas.
Get a saucepan going near the end of the tortilla pile. Put a big tub of sour cream in it, and an equal amount of "cream of >something< soup. It can be chicken, celery, mushroom, whatever. Heat that up until it's sort of bubbling and warm. Add in a bunch of cans of green chiles (however many you want).
The last part is just assembling them all. Get a big cake pan. Have your filling ready. Then you just dip the individual tortillas in the white sauce, blob some filing in them, roll them like cigars and nest them in the dish. I dump tons of shredded cheese on each layer, usually we cram 2-3 layers per dish. If you have leftover tortillas and sauce at the end you can dump the sauce on top and layer the leftover tortillas flat on it, then top with cheese.
Then you just bake it until the cheese is melted, and slightly browned on the edge. It won't take long if you bake it right away. You can also cover it and freeze the whole thing to bake another day. Another variation we do is to make and freeze it in a bunch of individual pyrex tupperware dishes, and then Robert can take those to work for lunch. Or I can pull one out and throw it in the microwave or stove when I need a fast meal. It's a lot cheaper than buying Amy's microwavable enchiladas all the time.