What really works for me is priming my brain with a problem (doing the research leg-work if you will), then taking a break. Going for a walk or some other menial task seems to work best.
During this time the problem will fester in my mind, ideas will shape up and fall down. It's important not to get distracted, this is an active-ish process.
When you come back home (very important is to at least the room where you started) you can begin putting words down on paper, or graphs or whatever, with a possible solution. This makes your thoughts really crystalize.
After that you really do have to try it out in practice. A lot of things that look great in your mind don't end up working as well within the constraints of The Real World.
During this time the problem will fester in my mind, ideas will shape up and fall down. It's important not to get distracted, this is an active-ish process.
When you come back home (very important is to at least the room where you started) you can begin putting words down on paper, or graphs or whatever, with a possible solution. This makes your thoughts really crystalize.
After that you really do have to try it out in practice. A lot of things that look great in your mind don't end up working as well within the constraints of The Real World.