The one thing that irks me, however, is that it seems like everything is very very chaotic.

That's a normal perspective for new viewers and it's the main reason hockey has so much trouble gaining traction in the US. If you keep watching, you'll start noticing the patterns and strategies. Hint: Try to focus on watching the players and not the puck.

To my eye, there does not seem to be any set plays either, or very rarely if there are.

Set plays are easily read (hockey players have been playing for 20+ years and know all the tricks) so general strategies are better to use in general. However, some of the top players with the best chemistry and playmaking ability (Crosby, Sedin twins, Thornton, Kovalchuk) can orchestrate set plays. You'll also see a lot more set plays on the powerplay, when the offensive team has more time and space to execute.

My question is. When teaching hockey to a young kid, or a amateur like me, what is the general strategy in this game?

Every coach is different, and every team executes slightly different strategies. However, as a general rule, passing is far more volatile and subject to bad bounces in hockey than it is in any other sport, so passing backwards in the defensive or neutral zone can be seen as too risky. One bad bounce and suddenly Zach Parise has a shorthanded breakaway. Also, it's far more difficult to change your direction of momentum on skates than it is on foot (unless you're Pavel Datsyuk), so it's best to keep the direction of the puck forward or lateral so that you don't have to scramble and possibly fall down. Keep the whole play in the peripheral vision of the entire team and you'll have a better chance of success.