Do I really understand the problem?
(a) What exactly does the input consist of?
(b) What exactly are the desired results or output?
(c) Can I construct an input example small enough to solve by hand? What happens when I try to solve it?
(d) How important is it to my application that I always find the optimal answer? Can I settle for something close to the optimal answer?
(e) How large is a typical instance of my problem? Will I be working on 10 items? 1,000 items? 1,000,000 items?
(f) How important is speed in my application? Must the problem be solved within one second? One minute? One hour? One day?
(g) How much time and effort can I invest in implementation? Will I be limited to simple algorithms that can be coded up in a day, or do I have the freedom to experiment with a couple of approaches and see which is best?
(h) Am I trying to solve a numerical problem? A graph algorithm problem? A geometric problem? A string problem? A set problem? Which formulation seems easiest?