It depends on how far, and where, you are riding. If you're just cruising around the neighbourhood for up to an hour, regular athletic clothing might be all right. If you're riding to the store or work in 20 minutes or less and aren't in a hurry, you could just wear what you have on at the time.
When you get into long rides of an hour or more, you might want to look into cycling-specific clothing for the comfort factor. Especially shorts.