Inspiration comes from knowledge and curiosity. The two can be combined in a great brainstorming session.

Here's what you do.

1. Sit down with a blank piece of paper. (It's always best to do this by hand rather than using a computer, tablet, or phone.)
2. Write down the question you are exploring. Always explore with questions. When you state a proposition, the brain often fights you. But when to put things into the form of a sentence, your brain goes into "search" mode.
3. Sit there and write down anything that comes to mind. Don't worry whether the idea is "good" or not. The point here is to be uncritical and let the ideas flow.
4. As the ideas accumulate, try to cluster related ideas together. And then start to indicate relationships with arrows. Try to write the fundamental ideas in bigger print, with underlines or bold face. In other words, try to show relationships on the page.
5. If the paper gets too messy, get a clean sheet and transfer your ideas with a better format. But don't stop brainstorming. Keep pushing. Keep adding ideas. You almost can't have too many.
6. This is important: When you get stuck, keep pushing. Dig deeper. You know more than you can immediately access. Your knowledge goes deep. Dig for it. If you remain stuck, rephrase questions and issues. Think about related ideas and examples.
7. Think also about opposites and exceptions. Don't be afraid of asking wild questions. Psychologists talk about "divergent" thinking. That means thinking that does not fit nice neat outlines and pre-set models. Be divergent!
8. Inspiration sometimes just "shows up," but not usually. You need to give yourself prompts and questions.