What is good advice for introducing kids to home improvement?
I'm young(ish) and still remember learning how to use power tools, so let me offer you a few thoughts from when I was learning:


I always find it helpful to hear about (or think about) what could go wrong. I.e. what's the danger that the user is trying to avoid. For example, a table saw is loud and scary, but what's really the dangerous situation you're trying to avoid? Answer: pinching the wood against the blade causing a kickback. OK, now that I know what the danger is, I'm better prepared to avoid that situation. (Just a single example; obviously a table saw has other dangers.)
I think the most dangerous tools are the ones that don't look scary. E.g. everybody knows that a chainsaw is a powerful and could kill you if you're not careful, but a hand-held router could actually cause some serious damage but they basically just look like a drill. Think about it: they've got powerful motors, long and sharp bits, are prone to grabbing the wood and kicking back if not careful, and can swing / fall / twist in pretty much any direction. Plus depending on how you're using it the bit may not even be visible.