I invented Cooperation Cube on a flight from Tokyo to Syracuse.
When I think back to that flight, three key ingredients stand out that I believe can be generalized for anyone trying to invent something new:
Have a High-Level Concept
I knew I wanted to create a "3D board game" - something physical, not just a flat board, and not merely an RPG or tabletop game with miniature characters.
If you don't have a high level concept, it's like playing charades without an initial word to act upon.
Articulate Your Taste (What Do You Like?)
There were elements and game mechanics I appreciated about the games I had played in the past:
Having this list of ingredients in mind provided me with a starting point, a puzzle to solve, intertwining these favored mechanics into a new, cohesive gameplay experience.
Put Yourself in a New Environment
It's vital to stimulate your senses with something new - a new place, sounds, and smells. However, it's not only about introducing new scenery. The environment also needs to be conducive to focus, enabling you to be alone and distraction-free so you can enter a state of deep concentration. For me, 13 hours alone on a flight did the trick.