Store a potato in a warm, dark location until it begins to form eyes. Cut one end of the potato that doesn't feature eyes so that the rest of the potato fits into a disposable clear plastic cup.
Insert the tips of three toothpicks evenly around the perimeter of the center of the potato. Set the toothpicks on the rim of the cup so that the lower portion of the remaining potato is suspended inside. Position the potato so that a few of its eyes face up and out of the cup so they can grow and form sprouts.
Pour cool water into the cup until it reaches 1 inch over the bottom of the potato.
Place the cup in a cool, dark location, such as a garage or pantry, for two weeks. Transfer the cup to a sunny spot, such as a windowsill or porch, when stems begin to grow from the sprouted eyes. Make sure the potato is partially submerged in the water the entire time you're growing the potato.