Writing, writing and more writing.
When I have something which needs to be examined or figured out I do that wonderful thing call introspection so I can pinpoint what it is I need to work on.
If it isn't a simple and quick answer I head over to my Live Journal to write about it. What's bothering me, what's feeling right, what I'm not sure about and just let my fingers do the talking. My brain sort of disconnects and my fingers, via the keyboard, just do their thing.
I might head over to xeromag to see if Franklin's written something about it or google it to get some differing ideas and opinions.
I'll go to some of my regular web haunts (here, PMM, any other related site) and see what they have to say on the subject.
I talk to my boyfriend about it when I feel the time is right. If the time isn't right I'll mention to Him that something's bothering me and I need to figure it out. He'll leave me be to figure things out. I'll bounce ideas off of Him since he's more logical and analytical than I am. Eventually the solution smacks me upside the head & says "i was there all along. You just HAD to analyze this, didn't you." lol
It's amazing what I figure out when I disengage my emotions from the equation and let the rest of me figure it out without all the emotional turmoil and upheaval.