The exposition of a story is the beginning part where most of the information regarding the play or story itself will be made known. An exposition will explain the who, where, and when right as it is happening, so that the reader can have a background on what is going on, or will happen next.
In the case of Saki's "The Open Window" the exposition takes place right as the story begins. The exposition also ends when the inciting event begins, or the moment when the action picks up. In this case, the action picks up when Vera says the words:
"Her great tragedy happened just three years ago," said the child; "that would be since your sister's time."
This being said, everything that occurs, and all that is mentioned right before that inciting event occurs, is considered to be the exposition.
Now, let's break the exposition by parts. To do this, you need to list all the information that you are able to gather from it:
1. "A very self-possessed lady of fifteen" is telling someone that her aunt will be in the house shortly.
2. This "someone" to whom she is speaking is Framton Nuttel, who is nervous to be there as he does not know the family.
3. He is there to take a cure for a nervous condition from which he suffers.
4. The woman whom he visits is Mrs. Sappleton. Nuttel's sister had written the letter of introduction that Nuttel is to give the lady of the house. The sister had assured him that the family was nice.
5. Framton confesses to the teen girl that he does not know anyone in town, which makes the girl curious.
This is the moment when she speaks about the supposed tragedy that her aunt suffered. This is the moment when the plot begins to move forward. Therefore, the five facts mentioned previously are the exposition of the story.
Remember that the purpose of an exposition is to set up the pace that will later be moved on by the inciting event and then will be heightened during the climax. Hence, often the description of an exposition is basically a tell-all of the place, the people, and the time.
The story is meant to be a scary one, but it is a comical story in which a Gothic, horror tale is nested. Hence, during the times that the story is told from the 3rd person objective point of view, the narrator, the story tends to take a more jovial mood judging from the strange character of Framton Nuttel.
When the story switches to first person omniscient subjective, which is Vera's point of view as narrator of the fake ghost tale, the story takes a gloomy and dark mood typical of a Gothic story where there isolation, combined supernatural events.