Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
Got My Pipe
Two guys sit in the dark, silently smoking. Yep, that's about it. C. Auguste Dupin, private detective, and his roommate, the unnamed narrator, are puffing away in a smoky reverie when G—, the head of the Paris police, enters the scene.
Conflict
A Mystery!
G— spends a lot of time rather cryptically explaining the mystery at hand. Basically, the crafty D— has made off with (purloined!) a secret and scandalous letter belong to some unnamed royal lady. He's now blackmailing her to get what he wants politically, and she's called in G— to purloin it back.
Complication
Search and Destroy
Every night for the past three months, G— has been searching D—'s hotel room for the letter. Thoroughly. How thoroughly? Try this:
We examined the rungs of every chair in the hotel, and, indeed, the jointings of every description of furniture, by the aid of a most powerful microscope. Had there been any traces of recent disturbance we should not have failed to detect it instantly. A single grain of gimlet-dust, for example, would have been as obvious as an apple. Any disorder in the glueing —any unusual gaping in the joints —would have sufficed to insure detection. (53)
All this, and still no luck. Meanwhile, the political situation isn't improving. So now we know why G— just so happened to show up at Dupin's door after an absence of several years: he needs help.
Climax
Message In a Fireplace
A month later, G— show up again still letter-less. Surprise! Dupin has it now, and sells it to G— for fifty thousand francs. G— gets what wants, Dupin shows off his massive brain, and the narrator's man-crush on Dupin gets just a little crushier.
Suspense
Get To the Point, Dude
Great! The letter is (presumably) on its way back to its rightful owner; it's been confirmed that Dupin is both smart and sneaky; and, best of all, we're finally about to know what's in this stinkin' letter. Right? Wrong. All the narrator wants to know is how his genius BFF came up with the answer, and for him the suspense is in waiting to find out how Dupin located it, rather than what it says.
Denouement
Unravel This
In the "Complication" phase of the plot, G— tells Dupin how he doesn't find the letter. Here, Dupin tells the narrator (but not G—) how he does find it. But don't think that there's any real resolution. In fact, what we end up with is just what you'd expect from unraveling ("denouement" means "unraveling") a piece of cloth: a whole bunch of loose ends.
Conclusion
To Be Continued…
At the very end, Dupin reveals that he purloined the letter because he (1) digs the royal lady on a political and possibly personal level, and (2) wants to get revenge on D—. Which, if you think about it, is totally weird. Throughout the entire story, we've assumed D— is just doing this out of boredom or (non)professional curiosity. Instead, the ending sets up the story as merely one installment of a long plot. If this were a Hollywood movie, you'd know to expect "The Purloined Letter II: The Return of D—" to be coming out next summer.