What is the best method to teach "The Open Window"?

One approach to teaching this story is to address the justification of Vera's lying. Framton Nuttel is a complete bore. His nervous condition may be self-induced or it may actually be legitimate. However, he is self-involved. He only talks about his ailments and therefore is largely focused on himself. That being said, readers might sympathize with Vera and conclude that Framton is a bore that is begging to be duped. On the other hand, Vera's prank is quite cruel. She could just as easily have given Framton a story of hope or some other romantic tale that might have raised his spirits. So, you might consider having a debate in class. One side argues that Framton is a self-involved bore who is too easily duped and is therefore fair game. The other side can argue that Vera is unnecessarily cruel. 

Another approach is to analyze the significance of names and other words in the story. Discuss the irony of Vera's name. "Vera" comes from "veracity" which means "truth." Nuttel suggests that Framton is a "nut." He is odd, crazy, or "nutty." Vera uses the window to create a story. So, we have a story (Vera's) within a story (Saki's). This "story within a story" is often called a "frame story." And here we have an actual frame: the frame of the window. Thus, the frame story (Vera's story) actually emerges from the open window.