Sometimes I find something particularly moving. It may be a spoken line or a characteristic of a person or a particular scene. It is compelling to me, but I have no idea what to do with it. I don't want to leave it alone or let it fade away, but I find myself asking, "How do I make this a story?"
The answer to that question will depend on the thing you are thinking of. To answer it, you will probably need to approach it from several angles. You will definitely need to know what else is going on beyond that fragment.
I find the easiest method is to work backward from it to find out what caused it. From there, the ending can be easily derived. Of course, if you do the exact opposite and figure out what happens after the thought, then the origins should fall into place.
Good thoughts are valuable. Sometimes a whole story just springs to mind, but when you only get a fragment, it's not worthless. Just ask that question and put in the effort to find out the answer.