Till the soil with a rototiller or loosen it with a shovel. Remove any rocks or roots and mix in enough compost or manure to lighten the soil.
Test the soil with a soil test kit. Soil pH should be between 6 and 7, so add lime to raise the pH or aluminum sulfate to lower it. Work the amendments into the top 4 to 6 inches of soil.
Use the hoe to dig rows 12 inches apart. Sow seeds 1/2 or 1/4 inch deep and 1/2 inch apart. Cover the seeds with soil and lightly sprinkle on a coat of all-purpose fertilizer and water after planting. The seeds will germinate within two weeks.
Thin seedlings when they're 2 inches tall by spacing 2 or 3 inches apart. Handle the radishes carefully to avoid damaging the roots.