In a bowl, add the cornmeal, salt, and water and mix until well combined. Let the mixture rest for 10 minutes. Using your hands, form 8 balls of the arepa dough. Flatten each ball until each is 1-inch thick.
In a skillet, heat oil over medium heat. Add 3-4 arepas at a time. Pan fry for about 5 minutes on each side until golden brown. Repeat with remaining oil until all the arepas are cooked.
Transfer arepas to a paper towel-lined plate to drain. Once they are cool enough to handle, cut a 4-inch pocket on the side of the arepa or cut in half. Add desired fillings. Serve and enjoy!