This puzzle was the topic of a thread in our Programming Diversions forum recently.
I think the point of this puzzle is that there is no methodology -- it's a "think outside the box" kind of puzzle. But for general problem solving, you might want to have a look at How to Solve It, by G. Polya. It's a wonderful little book which analyzes the various kinds of problems you might solve in mathematics and related fields.
I'm usually not very good at these, but figured it out after 5 or 6 throws. What's interesting is that even though I knew better, I couldn't keep my mind from trying to apply some overly-analytical solution.