Pour the oil into a heavy 10-inch skillet (the oil should be about 1/2 inch deep). Heat over medium to medium-high heat until the oil shimmers, about 8 minutes.
To make chips, slice the tortillas into 6 wedges. (Leave the tortillas whole if you’re making tostadas.) Cover a large swath of countertop with clean brown paper bags, newspaper, kitchen towels, or paper towels for draining.
To make chips, add about 10 tortilla pieces to the pan, one at a time, being careful not to crowd them (or else they will stick to one another). Fry each batch for 2 minutes: they will begin to puff and curl slightly and their bubbling will cease. Flip the chips (ideally, with tongs; if not, use 2 utensils) and fry for an additional 1 to 2 minutes on the second side, depending on the thickness of your tortillas. Adjust the heat as necessary to keep the chips from burning. The finished chips should be golden and crisp throughout.
Remove the chips with tongs or a slotted spoon into a small sieve or wire basket held over the pan, and let them drain for a moment to leave behind as much oil as possible.
Transfer the chips to the paper in a single layer, not touching, to drain, and salt to taste. Let them cool for about 3 minutesthey will crisp up as they cooland devour while still warm. Discard (or eat!) any chips that did not crisp up all the way through.
To make tostadas, fry the whole tortillas, one at a time, as above for about 2 minutes per side, until golden and crispy throughout, pressing down on them slightly from time to time as they fry. Drain well, letting excess oil drip into the pan from the fried tortilla, then transfer it to the paper-lined countertop.
Recipe from Can It, Bottle It, Smoke It by Karen Solomon/Ten Speed Press, 2011.