Cut the potato seeds into sections, each about the size of an egg and containing 2 or 3 buds ("eyes"). Put the seed cuttings in a cool, dark place for 1 or 2 days before planting.
Prepare a plastic tray or basket to serve as a hydroponic pot by drilling drainage holes around the sides. Set the holes 2 inches apart in a line running 2 inches from the bottom of the tray.
Fill the container up to about 1 inch from the top rim with perlite, and set the container outside for a full day in the direct sunshine, so as to soak up at least six hours of full sun.
Soak the perlite with water until it starts to trickle out of the drainage holes.
Push the potato cuttings down into the perlite, so that 1 inch of perlite covers them. Space the potato seed cuttings about 6 inches apart.
Cover your hydroponic pot with a transparent plastic lid until the sprouts appear after two weeks. This step conserves water.
Water the plants with a mix of water and plant food every 3 to 5 days, unless it rains. Mix 1 teaspoon of 20-20-20 fertilizer per gallon of water into your watering solution until the sprouts are about 18 inches tall. At that point, switch to a high potassium, 10-10-20 mixture.
Harvest the potatoes between 70 and 90 days after planting.