Mix water and salt, and taste before adding fat (butter or lard) and letting the fat warm in the water. Add cornmeal and mix until mass forms. Let sit for 10 minutes to hydrate cornmeal; it may seem a bit loose before it sits. The dough should be firmer after sitting, enough to hold indents in dough if squeezed, but not run or smooth out on its own. Adjust with cornmeal (to firm) or water (to loosen) as needed. If desired, add about a half cup of shredded cheese to the dough and mix in.
If you are making a single batch, it is easier to separate the dough into equal portions now.
If you are making a larger batch, it may just be easier to measure out pieces as you go (as long as you have enough filling, either meat, cheese, beans, vegetables or a combination).
Take each piece of dough (about ½ to ¾ of the size of a baseball) and flatten it into a ½-inch disk. As you start to get close to a ½ inch, start to make a concave bowl (use the bowl of water and oil to wet the dough as needed to prevent it from cracking or breaking). Place about ¼ cup of filling in the center and close the bowl of dough around the filling by gently squeezing the top together. Keep wetting your hands and pat the sphere into a ¾- to 1-inch disk, making sure to keep wetting the outside to prevent cracking. If the filling does puncture through the dough, you can tear off a piece from the edge and use the water to wet the dough like Play-Doh to mend the opening.
You are now ready to cook. Heat a sauté or other shallow pan just below medium. Add just enough oil to coat the bottom of the pan. Without crowding the pan, brown for four to six minutes per side until brown speckles have appeared. Flip and repeat. Once the arepas have cooked for three to four minutes they are ready to enjoy or, if you prefer, stuff with more wonderful fillings.