Radishes are generally very quick to mature and easily grown from seed - so they're a great choice for kids or first-time gardeners. They grow well in most climates, but you'll find radishes to have more top than root if they don't get at least 6 hours of sunlight a day. Sow radishes thinly, directly in the ground at about 1/4'' deep. They can be sown as soon as you can work the soil (a month or so before the last expected frost).
Radishes grown in mid-summer will usually have a spicier taste. That sharp radish-taste is due to glucosinolates, or mustard oils! It's a good idea to plant small crops of radishes ever 2 weeks or so, since radishes shrivel quickly when harvested and if left in the ground too long, they'll become cracked and woody. Winter radishes can be sown in mid-late summer and harvested in the fall.
While they may not look like it, radishes are actually related to cabbages, so they're susceptible to many of the same pests and diseases.