Johnathan,
You've gotten good advice, and advice from the best. The only thing I can add is, first, write what you can and all you can before the idea leaves your mind, or before the Muse moves on. Second, once you have captured the idea, no matter how inchoate or "crude" it may seem, start picking it apart: what does each component mean? how do the components relate to one another? what if...? (The "what if" is a prelude to all sorts of questions: what if this wasn't here? what if that were more important? what if this had not happened? what if it happened in a different order? The possibilities are endless.) Third, if you're stumped, put it away for a while, work on something else, come back to it. Pick a piece of it and write about that piece. It may be that the original idea was not meant to become story, but was meant to point you to something entirely different. Hope this helps.
David