I have material that I created in the past about various tropes, characters, gameplay elements, etc. that caught my interest in the past. To start a new game design project I need a focus - some inspiration or a request from a collaborator. When I have that focus it's kind of like building a mobile - the focus is the center-point, and I have to find balanced things to hang on it to make the whole thing spin interestingly and have harmonious colors. So I brainstorm to see if that focus gives me any new ideas, and I also brows through my old material to see what seems compatible or like the two ideas might strike interesting sparks off each other. I try to imagine playing the game (or reading the story, if I'm designing a story rather than a game).
I think design is a basically iterative process, so something like The Snowflake Method is a good starting point if anyone isn't familiar with iterative design yet.