Then, there are the other times, where the idea is somewhat More Abstract. Sometimes purely aesthetic -- if you tweaked Romeo and Juliet so that the twosome realized their only chance lay in escaping the stupid city, could you make a comedy of it? -- sometimes delving into other philosophical matters -- would one of those "mirror universes" where morality is inverted really work? Which have their own problems, and I think they're the worse.
Actually, that Romeo and Juliet example is a poor instance of this problem in one respect. A tweaked tale still would need many of the characters from the play, and much of the plot. It would be humorous to see whether you could get as many as possible, and stick as close as possible, in the revised story, particularly if you made it obvious that it was based on it. (Depends on where the muse goes, whether making it obvious is good.)
Even when the inspiration is aesthetic -- could I write a steampunk space opera? -- and still more on other matters, you start out with very little that's concrete. Characters, plot, setting -- even if the abstract idea has any of them, it does not have them in detail. Perhaps it's just me, that putting glasses on a girl makes her more concrete than, say, having her regard an arranged marriage as perfectly ordinary and certainly nothing to throw a fit about. Theme is particularly weak for issuing easily into these concrete things.
But the best way to go is to poke at the idea looking for Conflict (for plot) and Motivation (for characters). Taking your thematic notion, how can you find two characters who will be willing to fight over it? What is the situation that will inspire them to fight? And can you give sparkle and snap to their dialog passages, where both sides have to give their case? (The last is one of the harder ones, and if you succeed, you may find that your readers regard it as supporting the other side. sigh. Then, you don't want to shoot fish in a barrel, hard to build a story that way, and any concept that can produce conflict has probably not had all its issues thrashed out, so there are arguments to both sides.)
Then, there needs to be action as well as dialog. Talking heads do not a story make. (Aesthetic ideas, to do them justice, tend to lend themselves more readily to action.) What sort of actions would the conflicting views lead to? If nothing else, shouting your arguments while one character flees another keeps more drama in the scene. Even when they are just sniping at each other, it is wise to give them some busy work so they are not all talk. . . which applies still more when a character is thinking rather than talking.
(Yes, this is good advice for when you go and preach like I advised you not to. 0:)