Soak the folded paper towel in water and place in a glass. Cover tightly with cellophane and place on a sunny window sill. After 4 days, they sprouted nicely and are ready for planting. Fill planters (or styrofoam cups) nearly to the top with potting soil. Tip: To germinate cucumber seeds using water, wrap the cucumber seeds in a wet paper towel and place in a shallow bowl. Cover the bowl with plastic wrap, and leave it in a sunny and warm space. The cucumber seeds can germinate in as short a period as three days.