Slice the tofu into ⅛-inch-thick strips about 2 inches long, or into triangles, or slice it into ¼-inch-thick pieces (see the headnote). If your tofu is in a rectangular pan, slices are easier. If it is in a round pan, cut it into quarters, then slice each of them into triangular slices thin or thick as you please.
Pour 1½ to 2 inches of peanut oil into a deep fryer, stable wok, or wide shallow pot, and heat over high heat. When the oil reaches 360°F (if you don’t have a thermometer, stand a wooden chopstick or wooden spoon handle in the oil—if the oil bubbles up along the wood, it is at temperature). One at a time, slide the strips or triangles of tofu into the oil near the side of the pan; try to make sure that they are not overlapping. Working in batches, use a slotted spoon or a spider to separate any that are sticking together. Lower the heat to medium-high and keep moving the pieces around so they brown evenly; turn them over occasionally. After about 5 minutes, they should have changed color a little. Use tongs or a spider to lift them out of the hot oil, pausing to shake them a little and let excess oil drain off, and transfer to a paper-towel-lined plate. Repeat with the remaining tofu.
Serve hot or warm, on their own or with one or more dipping sauces.