To grow a potato plant with water and tooth picks, find a potato with at least one visible eye or sprout and a glass big enough to fit the diameter of the potato when standing on its end. Insert four toothpicks around the center of the potato so that the toothpicks hold the potato up by resting on the rim of the glass. Fill the glass with water and place it in a window that receives direct sunlight.
Remember to place the potato in the glass so that the visible sprouts or eyes face down into the water, or so that the largest grouping of sprouts are submerged in water. The water should cover about half of the potato. Potatoes need at least six hours of daylight a day to grow. Wait a few weeks for rootlets to emerge from the bottom of the potato and stems to grow from the top. Add more water as needed, and change the water if it turns brown or cloudy.
Potatoes eventually rot away when left growing in water. After the potato grows to about 8 inches, you can transfer it to a pot filled with soil to continue growing the plant. Fertilize the soil well, and keep it moist. Clip the new growing vines after they grow 10 inches to create a bushier plant.