The setting and time of the story seems to in a place like Florence or Venice, Italy, during the 17thC perhaps, and specifically during Carnival.
The narrator, Montresor, has suffered some kind of insult from a man named Fortunato. We don't know what the insult is, but it is sufficiently bad for Montresor to plan Fortunato's death. The best punishment, according to Montresor, is punishment "with impunity," that is, not getting caught. Montresor meets with Fortunato on the street (by design)--Fortunato is dressed as a jester, and Montresor has a silk mask and a black cloak to disguise his identity.
Montresor tells Fortunato that he has obtained a cask of a rare wine, Amontillado, but he isn't sure it's the real thing and he's on his way to see a man named Luchesi who can tell him if the wine is genuine. Fortunato, a pompous and proud man, tells Montresor that Luchesi knows nothing and that Fortunato will go with Montresor to taste the Amontillado--it's helpful that Fortunato is already slightly drunk.
Montresor, who has made sure his servants aren't at his palazzo, takes Fortunato down into the catacombs under his palazzo, stopping at various points on the way down to sample other wines to make sure Fortunato is as drunk as possible. Because Fortunato is coughing during their walk in the catacombs, Montresor, expressing an ironic concern for Fortunato's health, suggests that they turn around and go back. Fortunato, eager to drink the Amontillado, insists that they go on.
They finally reach the lowest level of the catacomb, and Fortunato asks where the Amontillado is. Montresor replies that it's in the back of a small alcove, and as soon as Fortunato steps into this small room, Montresor shackles him to the wall. At first, Fortunato, still very drunk, thinks this is a joke, but when Montresor uncovers his mason tools and mortar, Fortunato realizes his peril.
As Montresor finishes the wall, Fortunato begs him for release and then becomes quiet, perhaps mad, for the only response he makes to a question from Montresor is a slight jingling of the bells on his costume.
Montresor has lived up to his family's motto--loosely translated as "no one harms me with impunity"--because he has killed Montresor to repay him for the "insult" mentioned at the beginning of the story. The Montresor Coat-of-Arms shows a snake biting a foot that is stepping on it--a fitting depiction of how Montresor "bit" Fortunato. Most important, Montresor has punished Fortunato with impunity--no one will ever look for Fortunato in Montresor's catacombs.