Boil the potatoes until they are easily pierced with a knife, usually 20 to 25 minutes for larger potatoes. If desired, you can peel the potatoes beforehand.
Drain the potatoes in a colander. Reserve 1/2 cup of the cooking water for later use. Return the potatoes to the pot, and shake over medium heat until they are dry and mealy, usually three to five minutes.
Remove the potatoes from the pan and let them cool. Place a potato on the cutting board, and slice it into 1/4-inch rounds. Repeat for all potatoes.
Cut all 1/4-inch slices into small 1/4-inch squares. Place the squares into the cooking pot with the reserved cooking water.
Mash the potato squares inside the pot with a heavy fork or hand-masher. For smooth potatoes, work out lumps as best as possible. Add additional ingredients according to your favorite recipe.