How to Grow a Sweet Potato Plant Use toothpicks to suspend the sweet potato over a clear glass of water with the tip down, having enough water in the glass to cover the bottom of the sweet potato. Keep it in a warm, sunny spot. Soon vines with morning-glory-shaped leaves will appear and climb anywhere you train them. Keep the water level constant (covering just the bottom of the tuber). Change the water occasionally and DO NOT plant in soil. When the individual slips put out four to five leaves, you can snap the new plants off the mother potato.