Peel potatoes, and cut into desired size and shape. To make thick French fries, slice potatoes lengthwise into 1/4-inch slices, and cut again into 1/4-inch strips. For shoestring potatoes, use a mandoline fitted with the fine julienne blade. Make basket-weave-style fries by fitting the mandoline with the fluted cutting blade; rotate the potato 90 degrees between each pass over the blade. Place sliced potatoes in a large nonreactive bowl, and cover with water.
Drain potatoes, and dry thoroughly with a towel. Heat 3 to 4 inches oil in a heavy-bottomed pot over medium heat. Use a thermometer to ensure the temperature is correct: 325 degrees for French fries, 375 degrees for shoestring and basket-weave fries.
Carefully add potatoes to oil in small batches so as not to lower the temperature of the oil. Cook shoestring and basket-weave potatoes for 2 to 3 minutes, turning occasionally. French fries need to cook for 5 to 6 minutes, turning occasionally. They will not take on much color at this point.
Transfer to a flattened brown paper bag that has been lined with paper towels, and let cool for a few minutes or until just before ready to serve. French fries need to be fried a second time: Raise oil temperature to 375 degrees. and fry for until crisp and golden, about 1 to 2 minutes. Remove from oil, and drain again on the paper bag. Sprinkle with salt, and serve.