Till the soil in the garden bed to a depth of about 6 to 8 inches in early spring. Prepare to plant seed potatoes about three to four weeks before the average date of your last spring frost. This will loosen the soil and create a more hospitable environment for the potato plants. Dig a trench about 4 inches deep, 12 inches wide, and the length of each proposed row of potatoes. Add granulated, slow-release fertilizer to the trench, following the manufacturer's label directions regarding quantity and dosage. Scratch the fertilizer into the soil in the bottom of the trench with a garden claw or hoe.
Lay seed potatoes in the trench, spaced about 12 inches apart. Seed potatoes are regular potatoes, stored over the winter. In spring they're cut into pieces, ensuring each piece has an "eye" or growing point. Orient the seed potatoes so the eyes are facing up.
Cover the seed potatoes with a 6-inch layer of hay or straw.
Water the seed potatoes by placing a sprinkler in the garden bed. Run the sprinkler for one to two hours. Water with the sprinkler once a week if rainfall is scarce, so the potatoes receive the equivalent of 1 inch of rainfall per week.
Add more hay or straw when the tops of the potatoes grow to about 6 inches high, so only the top 3 inches of their growth is visible above the mulch. Continue adding more hay or straw as the plants grow, keeping the visible top growth to about 3 to 4 inches.
Harvest the potatoes at the end of the summer when the tops wilt and fall over. Use a pitchfork to gently turn the mulch over near the plants. The potatoes will roll right out of the mulch.