One good example of irony comes when Fortunato coughs in the catacomb from the damp air; Montresor seems to worry about his ill-health, and asks him to return to the surface:
"We will go back; you will be ill, and I cannot be responsible. Besides, there is Luchesi--"
"Enough," he said; "the cough's a mere nothing; it will not kill me. I shall not die of a cough."
"True -- true," I replied...
(Poe, "The Cask of Amontillado," eNotes eText)
Montresor shows that he is not even slightly worried that Fortunato will die of a cough. This is because Montresor is assured of his own role in Fortunato's death, and knows precisely what will actually kill him. The irony is that, in claiming concern for Fortunato's health, Montresor actually shows his personal assurance that the plan will play out as he intends, and is not worried that anything will interfere. Montresor is also not afraid to show hints of his plan, even displaying the trowel he will use to brick Fortunato into his tomb.