A dutch oven or high-sided cast iron pan are your best bets, as they retain heat well and have big sides to prevent splattering oil. This is cold oil, not hot, as this process heats up the oil and fries simultaneously. This simulates the double-fry method mentioned above. As the oil heats up it leaches moisture from the potato, which allows the later heat (once the oil is up to temperature) to actually fry the chip. The oil will begin to bubble up around the fries, which is a good sign. These bubbles aren't actually oil, but escaping water molecules. You should be able to easily pierce the potatoes with a fork. This means they've softened enough to really start frying. The bubbling in the oil should crank up significantly, and after 20-25 minutes you should notice that the fries are starting to get golden brown and delicious looking. A few more minutes and they'll be perfect. Remove the fries from the hot oil with a slotted spoon or wire strainer, then pat dry with paper towels. Don't let excess oil stick around -- it leads to soggy fries. Once you're done patting, season liberally with salt and serve.

Summary:
Layer your potatoes in a deep, heavy-bottomed pot. Cover the potatoes with at least one full inch of your oil. Cook for 15 minutes on medium heat. Mix up the fries with a wooden spoon and cook for another 25 minutes. Turn the heat to medium-high and cook until golden brown, about 20-30 minutes. Drain fries on a rimmed baking sheet lined with paper towels and salt immediately.