I can't claim to be any kind of genius myself but creative "breakthroughs" in my experience has mostly followed the same pattern: Immersion -> Gestation -> Creative Leap.
You start by immersing yourself into a problem, reading everything there's to read about the subject, getting all aspects of the problem down on paper, pondering it wherever you go etc. As you start this you will also start a subconcious gestation process where you're brain will start arranging itself to the problem space. This is why I think you see "obvious" solutions to problems after a certain period of time.
The "creative leap" or "aha!" moment can take different forms. I find they often pop into my head while doing something else like taking a walk or a bath and letting my mind drift. Exercise is also great to stimulate the brain. It can also come in the form on coming in contact with something in a different area and seeing how it relates to your problem.
I've found the more I know about a wide array of topics the easier it is to find creative solutions to stuff. Learning stuff like languages and playing instruments also creates new cross-connections in the brain. What you eat will also to some degree have an impact on your thought process so eat some nuts and fish :)
Some other good habit is to constantly re-examine and question "basic facts" and "certainties". Keep a text dump of your thoughts so you easier can arrange and go back to them. Play "pretend it's magic", "if it/you could anything, what would it do?". Assume there's a solution and speculate around it's properties instead of questioning whether one exists.
So immerse yourself, eat well, learn about lots of stuff, take long walks, exercise and don't be afraid to daydream :)