On a windy, fall night in Paris, sometime in the 1800s, the narrator and C. Auguste Dupin are smoking pipes in the dark, thinking their thoughts. Suddenly, G—, the head of the Paris police, enters. Do they want to hear a mystery? Do they ever! So G— tells a story:
A few months ago the royal lady (probably the queen) gets a letter. She's in her sitting room reading it when another royal person walks in (probably the king). She wants to hide the letter from him, but she can't get it into the desk drawer fast enough. Instead, she puts it on the desk, with the address showing.
In strolls dangerous Minister D—. He notices who the letter is from (the readers aren't told), notices that the royal lady is acting funny, and realizes she wants to hide the letter from the royal man. Right in front of everyone, D— switches the royal lady's letter with one of his own and walks out. The lady can't stop him, because she's afraid D— will show her letter to the royal man.
So, now he's using the letter to make the queen grant some vague but no doubt nefarious political wishes. Enter G—, whom she's called in to find the letter for her. Thinking that D— must have the letter either on his body or in his home, G— has searched and search—like, every night for the past three months—and still found nothing.
Dupin takes an interest, asking G— to describe the letter, inside and out. Finally, G— leaves, resolved to search again. About a month later, he comes back. Still no luck. By this point, he's totally frustrated and offers to pay fifty thousand francs of his own money to whomever can find that letter.
Great! Dupin says—and hands over the letter.
After G— leaves (50,000 francs poorer, but stoked about the promotion this probably means for him), Dupin tells our narrator how he found the letter:
He knows that D— is smart, definitely smart enough to have known how and where G— would search for the letter. He concludes that D— probably hid the letter out in the open, where G— (who's not so smart) would never think to look.
So he waltzes over to D—'s house for a friendly little visit, wearing green glasses to hide his eyes. He sees the letter, disguised as another letter, in an organizer box hanging from the fireplace. The next day he returns with a copy of the disguised letter. Dupin then creates a distraction in the street, so that D— wouldn't notice as he swaps the copy for the original. The final touch? Inside the fake letter, Dupin wrote a snide little note to gloat about how he's outsmarted D—.