Which "mean" to use and when?

So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean and it's application to 'speed' related problems). However, a question that has always intrigued me is "how do I decide which mean is the most appropriate to use in a given context?" There must be at least some rule of thumb to help understand the applicability and yet the most common answer I've come across is: "It depends" (but on what?). This may seem to be a rather trivial question but even high-school texts failed to explain this -- they only provide mathematical definitions! I prefer an English explanation over a mathematical one -- simple test would be "would your mom/child understand it?"