It depends how complicated you want to make it. There are styles where the potato (or apple etc) is placed on a pin, and with a hand crank, the blade works through the potato as the hand crank spins the potato and moves it incrementally closer to the blade (creating the spiral effect). There are also much simpler methods using a corkscrew type center attached to a very sharp blade and handle. Then the corkscrew part is "screwed" into the potato at one end and by continuing to turn, the blade cuts in the spiral shape. That's probably the simplest. Here's a link to see an image of the easier method (the more complicated version can be found through google, and looks much like a hand crank peeler that comes with the spiral cutter).
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+1, the second method is what I was going to suggest. The threads pull the device through the potato and blade cuts a spiral path.
Where are you growing these spiral potatoes?