Theclimax of the story is when Montesor chains Fortunato to the catacomb wall and seals him down there with a brick wall.  The entire thing is done while Fortunato is begging for his life.  

The resolution is Montresor calmly telling his readers about his deed 50 years later.  He also admits that nobody has ever found the body, and that he feels no guilt over the entire thing. 

The initial key plot point is the circumstance which establishes conflict: The narrator, Montresor, feels that he must seek revenge on Fortunato for a "thousand injuries" he has suffered due to Fortunato's influence. He never explains exactly what these thousand injuries entail, and that makes him suspect for being an unreliable narrator.

The next key plot point arises when Montresor lures Fortunato to the place of his death. He knows that Fortunato is a prideful man and pointedly mentions that he has purchased a cask of amontillado; however, he's unsure of it's authenticity. He assesses Fortunato's personality correctly, and the man pridefully agrees to accompany him and taste this amontillado himself.

Inside the catacombs belonging to Montresor where the amontillado is supposedly stored, Fortunato begins coughing, and Montresor offers to take him home, telling him that he will be missed. Fortunato declines, intent on completing this task.

As Fortunato steps inside a small recess, Montresor chains him to a wall. Fortunato is taken completely by surprise and doesn't understand what is happening.

Montresor begins walling up this small recess, creating a crypt for his prisoner. At this point, Fortunato realizes what is happening and begins screaming. No help comes for him, although Montresor briefly considers the possibility that his screams might be heard.

Around midnight, Montresor has only one stone left to add to the new wall when Fortunato comments that it's time to end Montresor's little joke and allow him to leave. When Montresor replies that it is time to be "gone," Fortunato realizes that Montresor is serious.

Montresor finishes the wall and has lived for a half of a century knowing that he made Fortunato disappear without personal consequence.

The main plot of Edgar Allan Poe’s story “The Cask of Amontillado” is easy to describe. Montresor, a wealthy man, feels that he has been insulted by another man named Fortunato. The precise nature of the insult is never revealed, but Montresor considers it serious enough that he intends to kill Fortunato in retaliation. Knowing that Fortunato regards himself as an expert about wines, Montresor allows Fortunato to think that he (Montresor) may have been deceived by a third person (Luchesi) about the purchase of some amontillado wine. Fortunato then insists on traveling deep into Montresor’s underground wine faults to see and taste the amontillado. Montresor is only too happy to let Fortunato undertake this journey. Ultimately he buries Fortunato alive.

Some elements of this basic storyline are especially noteworthy, including the following:

• In the very beginning of the story, Montresor not only explains his desire for revenge but also addresses an unnamed “you” to whom he explains his plans:

The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult, I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.

Who, exactly, is Montresor addressing here?  Why does he feel comfortable confessing murder to this unnamed person?  In what senses does this person know well the nature of his “soul”? Is it possible that the person addressed here is a priest? If so, why does Montresor not express greater guilt for having killed another person? What leads Montresor to confess a crime committed (as we learn later) so many years ago? These are just a few of the questions provoked by the story’s second sentence – a sentence that immensely complicates the nature of the tale. If Montresor had made no mention of a person he was addressing – if he had simply launched into his tale – the story would seem much simpler and much less provocative.

• Equally interesting is the fact that Montresor never reveals exactly how and why he felt insulted by Fortunato.  What kind of insult could have been so great that it would justify retaliatory murder?  By leaving this element of the plot obscure, Poe contributes to the mystery of the story. We are left guessing about the nature of the insult.
• At one point Montresor confesses fear when he hears Fortunato screaming.  Presumably he is afraid that Fortunato will be heard and that the crime will be discovered and prevented:

A succession of loud and shrill screams, bursting suddenly from the throat of the chained form, seemed to thrust me violently back. For a brief moment I hesitated—I trembled. Unsheathing my rapier, I began to grope with it about the recess; but the thought of an instant reassured me.

Is it possible, however, that Montresor is frightened in some deeper sense? Is it possible that he is feeling guilt about his actions?

• Near the very end of the story, Montresor reports,

My heart grew sick on account of the dampness of the catacombs.

Is this the full or only reason that his heart grew sick?  Does it possibly grow sick in part because of an attack of conscience?  Once again, we are left to wonder. The plot of the story is basically simple, but Poe complicates the plot in a variety of interesting ways.

Many of the steps in the plot actually take place before the story begins, and are mentioned by Montresor as a means of explaining or justifying what is taking place during the height of the action.

Montresor has been insulted in some way by Fortunato, and he means to take revenge upon him, but must do so in a way that won't draw suspicion to himself. Therefore, he arranges for all of his servants to be out of the house during the Carnival, a party encompassing the entire city, so that he will have a private place to take his revenge with no witnesses and no evidence. He arranges a space in the catacombs beneath his house to bury Fortunato alive.

He meets Fortunato on the street, and Fortunato is already drunk. Montresor provides an engrossing lie about a valuable and rare wine (the Amontillado) that he wants Fortunato to examine. Fortunato agrees, and ignores Montresor's many warnings about the dampness of the catacombs and the threat they pose to his health. 

Montresor amuses himself with this and other veiled threats and notes of dark humor as he leads Fortunato deeper into the catacombs and closer to his doom. Once they reach the final location, Montresor chains Fortunato to the walls and begins to brick him up inside them. 

As much as Montresor wants to hear Fortunato's desperate cries and taunt him, his "heart grows sick" which he blames on the dampness, and he finishes his work and leaves. Fortunato's remains lie behind the wall for more than 50 years, with no one ever finding them.