This is an art. Anyone who appreciates REAL tacos, can understand that this is not easy. God Bless anybody that can pull this off accurately!
I have it down to a science. I learned from my grandfather. His biggest secret was in the fork you use. We use cooking forks. 3 prong cooking forks (most of the ones I see on google have two prongs). You can use regular forks too, but they arent made for cooking in high temp oil.
First you must get the oil HOT. 350 atleast, preferably 400 degrees. Just before it starts smoking. You need really high oil heat.
Once the oil is PLENTY hot, you hold a tortilla in one hand, and drop it in the oil halfway. It should be at 90 degrees, with your hand still holding the dry half of the tortilla. (Note: keep your cooking fork ready for the next steps)
If your oil is hot enough, it will cook that half of the tortilla almost instantly. Let it cook until it hardens up, which should be less than a minute.
Once the first half the bent tortilla is crisp, use the cooking fork to grab the tortilla half that is crisp and cooked. You will flip it here, putting the dry tortilla half (that was in your hand) into the oil, while the cooked half, sits above the oil with your fork. Now it should cook the other half of the taco shell.
The art is using the fork well enough to create a gap at the base of the shell (for meat or whatever you stuff with). And then flipping it and holding it with the fork while the other side crispens and finishes up.
I would like to make a youtube video that shows this process, and it truly is an artform. Many people make great tacos but horrible tortilla shells. I grew up near Mexico, I was born 4 miles from Matamoros. I have seen my share of taco cooking, in the strangest of places. The best tacos Ive ever had use this method. And the best taco makers Ive ever seen wouldnt do this any other way (by hand).
It's hard to do this without burning your hand(s). Be careful. The dry tortilla absorbs the hot oil, even when your holding it over the grease in the first step. Youd be surprised how a corn tortilla will drink the oil right up to your hand.
Give it practice. You will mess up a few tortillas. Dont worry about that, they make great quesadillas or nachos :)
Folding a burrito is serious business. Get it wrong and you'll end up dumping most of the contents all over the place and look like a burrito noob. Get it right and your hands and plate will be perfectly clean, and you'll no longer be hungry. Beware: publicly flaunting these skills might lead to people wanting you to fold their burritos for them.
General Tips
First off: make sure your tortilla is ready to be folded. A cold or dried out tortilla is likely to crack or split. Use a warm and moist tortilla.
Second: don't overfill the tortilla. If you have small tortillas don't try to make a giant burrito and expect that to work.
How to fold
Now that we have the basics out of the way let's get to folding. See the flash animation at Chow.com (which I've converted into an image here):
Place the contents in the approximately center of your partially folded tortilla. Leave plenty of room on the ends otherwise you'll most surely have food spilling out once it's folded up. Hold the filled tortilla so the weight of the filling pulls it tight. If your burrito busts through now, it will certainly burst later. If not, proceed to step 2.
Fold one end towards the center.
Fold the other end over.
Roll the bottom (the end nearest you) up towards the top. This isn't the intuitive way, but it's the right way. Make sure not to let the food squeeze out. I hold it with my fingers at the crease where the bottom edge that's been folded up meets the food.
Keep rolling it up.
Om nom nom.
Best Answer
Don't cut it up before cooking, do it after cooking. This is a common issue with many Mexican style recipes
Coat the fish with your spice mix, and cook as desired. When done, cut into cubes/chunks or flake onto your tortilla
Usually thinner fillets work best for this style in regards to surface area exposed to spices etc
Do the same for beef tortilla, spice and cook a steak, then slice it up thin and add it to your tortilla