Loosen the top 8 inches of soil in the garden bed with a spade or hoe. Work a 1-inch layer of compost into the loosened soil.
Sow the leek seeds to a 1/2-inch depth and space the seeds 3 inches apart. Space each row of leeks 8 inches apart.
Mist the soil, as needed, to keep the top 2 to 3 inches moist during the germination period. Frequent watering usually isn't necessary since leeks are sown during the cool, moist season. Seeds usually germinate in seven to 14 days.
Thin out the seedlings after they emerge so the remaining plants are spaced 4 to 6 inches apart in the row. Continue to water the bed, as needed, to keep the soil moist.
Place a toilet paper tube over each leek seedling once it reaches 3 to 4 inches in height. Nestle the bottom inch of the tube into the soil to hold it in place.
Pull up soil from between the rows of seedlings and mound it against the sides of the paper tubes to further anchor them in place and prevent the sun from reaching the base of the stalks. Remove the tubes and harvest the leeks once the stalks reach a diameter of 1 inch, usually within 60 to 120 days of planting, depending on the variety.