How do you know key points of the story?

The "key points" in any argument should be supported by the majority of the evidence presented and form the core of the summary or objective of the work. For example, if you had to summarize a 1,000 Word essay in 200 Words you ought to wind up stating the key points. If an essay (or other form of argument or report) was a kind of chair, the key points would be the legs holding it up. Exactly what any particular instructor means by the "key points" in an essay for scholastic purposes can vary, of course. So the best authority in such a case is the teacher.