How to think like a designer: Don't just observe the world, but draw upon what you know, interpret what you find, and look for unmet needs
There's a wonderful New Yorker article titled "The Eureka Hunt" (PDF). It's the story of a firefighter named Wagner Dodge who survived an out-of-control fire in the Mann Gulch in Montana in 1949. Thirteen other smoke jumpers died in the fire, but Dodge was saved by a brilliant insight. Fleeing for his life, he suddenly stopped running and ignited the ground around him. He then lay down on the smoldering embers and inhaled the thin layer of oxygen clinging to the ground. The fire passed over him and, after several terrifying minutes, Dodge emerged from the ashes, virtually unscathed.
What sort of a crazy person stops running from a fire and starts another one? Well, if you know certain things about fire and oxygen—knowledge that may have taken years to acquire—it's not as nutty as it sounds. Dodge had been a firefighter for many years and knew that fire needs three things to exist: fuel, air, and heat. By getting rid of the grass (i.e. fuel) around him, he took his chances with the fast moving fire and was able to save himself.
At first glance, insights like this one may seem to come out of nowhere. But in hindsight they make perfect, logical sense. What happens is that we (sometimes unconsciously) recognize patterns that enable us to see things in a new way. Albert Einstein put it succinctly when he said insight "comes suddenly and in a rather intuitive way. But intuition is nothing but the outcome of earlier intellectual experience."