Prep the soil in your garden plot. Remove the weeds. Dig the soil at least 12 inches deep and turn it. Break up any large clods and remove large stones. Test the soil pH, which should be about 5 to 5.5. Add any amendments and fertilizer, such as decomposed compost, pine straw, cottonseed meal, bone meal and kelp meal.
Select potato seeds. These are ideally chosen from organic farmers or nurseries with good reputations. You can find white, red, yellow and other varieties. Check to be sure the "seeds," which are actually tubers, look healthy and show no signs of softness, rot, mold, blackening or scabbing. The potatoes should be good looking, firm, somewhat small and not sprouting.
Cut the potato seeds into quarters, with one to three "eyes" in each section. Let them dry for a couple days to allow the skin to brown slightly.
Plant the seed sections directly into your garden. Place them several inches deep and 12 to 15 inches apart. Cover with soil, tamp the soil down lightly and water the garden.
Fill the area beneath the growing plants with more soil or straw as they begin to grow. You can create mounds, too, leaving the top parts of the plants showing. The higher the mound, the deeper your supply of crop at harvest time. Planting is usually in the summer for early or new potatoes, and in the fall for those you want to store.
Keep the garden watered, fertilized and attended through the season. Remove unnecessary weeds, and add straw between rows, if desired. This helps keep weeds down and also lessens mud splatter when watering. The straw can later be removed or tilled into the ground for even better soil the next year.