Rototill the radish bed to a depth of at least six inches. Submit a soil sample to your university extension to ensure that the soil pH is between 5.8 and 6.8. Withhold additional amendments unless the soil test shows a deficiency. Improve drainage if standing water is a problem by working compost or leaf mulch into the bed with the rototiller.
Check the soil temperature with a probe thermometer. Plant your radish seeds when the temperature is at least 55 degrees Fahrenheit, about 6 weeks before the last frost date. Sow seeds about a half-inch deep and 1-inch apart in rows. Space rows 12 inches apart. Prolong the harvest by planting new seeds when seedlings emerge, about every 4 days.
Thin young radishes to allow about 2 inches of space between plants. Use the young, thinned radishes for fresh eating. Check the growth of the radish root by lifting the leaves -- part of the radish will be sticking out of the soil. Harvest purple plum radishes 28 to 30 days after planting, or once the individual roots reach about 1 inch in diameter.