What to wear during triathlon?

I know about wetsuits. What I want to know is what do you wear under wetsuits. Or if wetsuit aren't allowed, what else do you wear? Do you wear a normal swim suit( I have Jammers) or pull on bike shorts over it for the bike and pull them off for the run? Or do most people just get trishorts/trisuits. I have heard you shouldn't run or swim in bike shorts. Also, how does the course length factor in to such decisions?