The story's opening sentence explains Montresor's objective.
The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult, I vowed revenge.
Montresor goes on to explain that he wants to punish Fortunato with impunity. As the story progresses it becomes evident that he wants to lure Fortunato into the catacombs beneath his palazzo and murder him. Montresor's problems in achieving his revenge make up the story's main conflict. He lies about having bought a "pipe" (i.e., 126 gallons) of Amontillado in order to entice Fortunato to his death. Fortunato is drunk, which helps a lot to deceive him, and Montresor keeps him drunk by giving him two bottles of French wine from his cellar when he gets him down the stairs.
One of Montresor's chief concerns is not to be recognized as Fortunato's companion. Poe achieves this through a stroke of genius. He makes Fortunato extremely conspicuous in a jester's costume with a cap and jingling bells. But this works in Montresor's favor. Fortunato is so conspicuous that no one notices his companion at all. Montresor is wearing a black cloak and a black mask. He must seem like a shadow of the boisterous and drunken jester.
Montresor must keep Fortunato following him through the catacombs to the niche where he plans to entomb him. He uses reverse psychology, urging him to turn back, knowing that this will have the opposite effect. For example:
"Come," I said with decision, we will go back; your health is precious. You are rich, respected, admired, beloved; you are happy as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill and I cannot be responsible. Besides, there is Luchesi" --
"Enough," he said, "the cough is a mere nothing; it will not kill me. I shall not die of a cough."
Poe invented the cough to keep Fortunato from asking a lot of obvious questions about this Amontillado. Where did he buy it? How much did he pay? Where in Spain did it come from?
The climax to the story comes when Montresor has achieved his objective and solved his problem.
From one of these [iron staples] depended a short chain, from the other a padlock. Throwing the links about his waist, it was but the work of a few seconds to secure it. He was too much astounded to resist. Withdrawing the key I stepped back from the recess.
Montresor still has to build the wall, but Poe covers this complex business with just a few sentences. The mortar is already prepared and has been kept moist by being covered with wet bones. After reaching the climax, Poe wants to wrap up the story as quickly as possible. Montresor specified that an essential part of revenge was to have the victim recognize the "redresser."
A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
Fortunato has been quite drunk to this point, but he sobers up quickly when he realizes what has happened to him. Here Poe has him call Montresor by name for the only time in the story. This is in order to prove that the sober Fortunato understands what is happening to him and who is causing it. Fortunato's cry is printed in capital letters in the text:
"FOR THE LOVE OF GOD, MONTRESOR!"
When Montresor replies:
"Yes, I said, "for the love of God!"
he seems to be implying that that cry for mercy is what he had expected and exactly what he wanted to achieve complete satisfaction.