Saki's story "The Open Window" is a great study on the social conventions of the Edwardians, as it presents the plot within a set of circumstances that are very unique to that era (1901-1910, think "Downton Abbey" toward the end of the first season).
The character of the young teenage girl, Vera, uses those very social conventions of the time as the springboard that will propel her to execute her mischievous trick upon the nervous Frampton Nuttel.
The first social convention that we can extrapolate, right from the start, is the old tradition of visiting the country for "a cure." In this case, Frampton had just suffered a nervous breakdown and needed to retire to a calm and quiet place to rest.
The doctors agree in ordering me complete rest, an absence of mental excitement, and avoidance of anything in the nature of violent physical exercise.
The visits to the rural side of England were thought to be therapeutic, as London was literally the cosmopolitan capital of the world with a bursting metropolis that was as busy as it was chaotic.
Saki, who was quite familiar with the London scene himself, surely evoked the neurosis of the typical Edwardian cosmopolite with the old-time paradigm of the bucolic and peaceful life in the countryside. However, he will show us that life in the country may not be as idyllic, peaceful or innocent as people make it out to be. This is Saki at his best satirizing his social peers and their pre-conceived notions of life.
The second convention is that these visits to the country are not necessarily between people who know each other. In this case, Frampton was visiting Mrs. Sappleton, whom he did not know, and he was also going to spend a good deal of time in her home.
How could these visits take place? Enter the third social convention in the story: the introduction letter. Frampton's sister is presumably the person who has ties with Mrs. Sappleton. She must have trusted her friend enough to propose the invitation of a third party to stay at her residence.
Moreover, Frampton's sister must have also trusted her brother's own behavior to even establish a connection with someone in the country for something as delicate as a resting cure. It is either that, or she purposely sent Frampton to the Sappleton's knowing that he would end up in some embarrassing situation. That, we will never know. However, knowing Saki's style, that is not entirely impossible.
Once in the country, Frampton makes the acquaintance of Mrs. Sappleton's 15-year old niece, Vera, who is in the parlor at the time he arrives. Another convention, he is there in order to get properly introduced to the lady of the house. But this does not happen because the young woman, true to her status as a young lady, uses her decorum to "warn" her house guest about her aunt's alleged trauma over her dead husband. She also uses this poise and decorum to quietly examine the new house guest and get his weakest traits.
On that note, we can assume that Nuttel (as his name hints) may have looked the part of a person with a mental issue. We can also safely assume that the young girl had the upper hand, being that she is quite well in control of herself. This is how she managed to tell the fake story of the aunt's dead husband, explaining that there is a reason for the French window in the parlor to be always open: for her aunt to wait for that dead husband to come back at any minute from the hunting trip that killed him and her (Mrs. Sappleton's) two brothers.
A final convention is the entrance of Mrs. Sappleton to meet Mr. Nuttel, and her asking him whether Vera was a polite hostess to him, as she is expected to be.
We know the rest. Nuttel's answer is that Vera was "very interesting". Shortly after that, the sight of Mrs. Sappleton's (very much alive) husband and brothers in law coming back from their hunting trip sends Frampton Nuttel into a frenzy, and he runs out of the house. Vera attributes this to a (false) "fear of dogs" and Mrs. Stappleton is left wondering what ever could have caused such reaction.
Therefore Saki conveys the social conventions of the time in a way that is both satirical and illustrative of how things were done. However, the satirical part of it is what Saki does best, always creating something unexpected from an otherwise predictable and foreseeable event such as a visit to the country to get a cure for an ailment.