Brainstorm the possibilities
Once the topic is decided, I find that a mind map is the best tool to expand upon the idea. Note that in many cases, after spending a few minutes mind mapping an idea, the best conclusion may be to discard the idea.
Though I prefer to use mind mapping for this step, you might prefer index cards, paper, a white board or outlines. Remember, the key here is to let your thoughts go wild without censor. Try not to structure your ideas at this point. Just do a brain dump focusing on the topic.
For digital mind mapping, my current tool of choice is MindNode on Mac OS X and iThoughts on iOS. I’m not sure what’s good on Android, so I’d appreciate your suggestions in the comments.