Peel the potatoes. Cut potatoes into 1/3- to 1/2-inch chunks as follows: Cut the potato lengthwise, then cut it lengthwise again. You should have four long pieces. Now, cut each of those into 3 to 4 pieces, cutting crosswise. This should give you nice bite-sized pieces, small enough to use a toothpick to skewer. Sprinkle with salt.
Pour olive oil into a wide, deep frying pan with a heavy bottom. Heat the oil on medium-high heat until hot. To test the oil, carefully place one piece of potato in the oil–it is hot enough if the potato immediately fries. If there is no bubbling/frying, the oil has not reached the correct temperature and the potato will absorb too much oil.
Carefully place the potato pieces in the hot oil and fry until golden, about 10 minutes. You may need to do this in batches since you don’t want to crowd the pan. Use a slotted spoon or spatula to remove potatoes and set them aside on a paper towel to drain.