I came up through the advertising ranks as a writer, broadcast producer and a creative director. This background gave me the skills I use as a CSD.
My background as a creative director has provided me with an intimate knowledge of the creative process, which is key, I think to being a successful CSD. You have to understand all components that go into producing good work: Sufficient Time, Sufficient Budget, the Correct Skill Set(s), and you have to understand that good creative is the result of a process - not something that is simply pulled out of mid-air.
As for special training or education, it probably doesn't hurt to have a creative background. At the very least, you should have some solid project management experience under your belt. You will also find it helpful, depending on the type of work you will be managing, to have some knowledge of printing, the Web, and/or broadcast production.
For me, transitioning from a Creative Director to a CSD was an easy move to make.