Purchase elephant garlic bulbs at a garden supply center in October or November. Although elephant garlic can be planted in early spring, a fall planting will provide an earlier start, and the garlic will grow rapidly when spring arrives. Select firm, large cloves that are free of blemishes and soft spots. Leave the bulbs intact, and don't divide them until planting time.
Till the soil to a depth of 10 to 12 inches. Add 3 to 4 inches of organic material such as compost or decomposed manure, and a balanced, granular fertilizer, applied at a rate of 2 pounds of fertilizer for every 100 square feet of soil. Work the organic material and granular fertilizer into the soil.
Use a hoe to create rows 18 to 20 inches apart. Divide the elephant garlic into cloves, and plant the cloves 1 to 2 inches deep in the soil, with the pointed end up. Allow 8 to 10 inches between each clove.
Water the elephant garlic deeply every eight to 10 days in spring and early summer. Withhold water when the tops of the plants begin to turn dry in July and August.
Remove any flowers that appear on the top of the elephant garlic plant in hot weather. Removing the flowers will prevent the elephant garlic from going to seed.
Harvest the elephant garlic after the tops die down in late summer. Dig the bulbs with a garden fork and place the garlic in the shade to dry for at least a week. Trim the stems down to 1 inch, and remove the roots. Store the elephant garlic in a dry place with temperatures of 40 to 50 degrees F.