Compost. Watermelon plants grow best in fertile, moist, well-draining soil. Compost helps accomplish this by improving soil structure, adding micronutrients and improving the soil's ability to stay moist and hold onto nutrients.ompost. Watermelon plants grow best in fertile, moist, well-draining soil. Compost helps accomplish this by improving soil structure, adding micronutrients and improving the soil's ability to stay moist and hold onto nutrients.