Select a self-watering container that is at least 18 inches deep to accommodate the watermelon's root system. Fill the container's reservoir with water.
Fill the container with potting soil. Insert the watermelon seed into the soil at a depth of 1 inch, then cover the seed with soil. Water the soil until it settles.
Place the self-watering container in a warm spot that gets full sun. Set a 6-foot trellis next to the container. As the vining watermelon grows, tie the vine to the trellis loosely with twist ties.
Refill the container's reservoir with water once a week. This ensures the reservoir never becomes dry. When the plant sets fruit, let the reservoir dry out until the fruit is ripe and you harvest it.