The essence of dramatic irony is that something is not understood by a character in the play or story which is understood by the audience or the reader. There is nothing that Montresor does not understand, so it must be Fortunato who is the target of dramatic irony. There are many examples of this.
Fortunato is wearing a jester's costume when Montresor encounters him on the street celebrating the carnival. Montresor says, "How remarkably well you are looking to-day." The reader knows Montresor thinks Fortunato looks like a fool and that this is appropriate because he intends to make a fool of Fortunato.
Fortunato does not know how truthfully he himself is speaking when Montresor urges him to turn back and he responds:
“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...
The reader knows full well that Fortunato is going to die, but not of a cold or a cough.
A good example of dramatic irony occurs when Montresor tells Fortunato he is also a mason. Fortunato asks for a sign.
“It is this,” I answered, producing from beneath the folds of my roquelaire a trowel.
Fortunato will not understand that Montresor has lured him down here with the intention of murdering him, but the reader understands this all along. When Fortunato sees the trowel he is surprised but he does not understand why Montresor should be carrying it. At this point the reader understands that the trowel will be used as part of the murder plot, but the reader does not yet understand exactly what Montresor intends to do to his victim. Montresor is acting with such brazenness because he is a little bit drunk and because he knows he already has Fortunato at his mercy. Fortunato is unarmed, while Montresor has a rapier. Fortunato is totally drunk and could not defend himself. He is already as good as dead.
Poe's use of irony is subtle because the reader knows what is going to happen but does not understand exactly how it is going to happen until it actually happens. Montresor finally makes his intentions obvious to the reader at the point where he says:
A moment more and I had fettered him to the granite. In its surface were two iron staples, distant from each other about two feet, horizontally. From one of these depended a short chain, from the other a padlock.
Another example of dramatic irony which runs throughout the story is that Fortunato is eager to taste the Amontillado and the reader knows--or at least is very sure--that this cask of Amontillado does not exist. Fortunato probably has no intention of telling Montresor the truth if he finds that the Amontillado is genuine. He is only interested in the wine because Montresor says he got a bargain. Fortunato would like to buy some for himself. We know he is thinking of putting on a show of tasting the wine, making the facial expressions of a connoisseur, trying another sop, and finally shaking his head and telling Montresor that it is only ordinary sherry. He intends to fool Montresor--but he has fooled him too many times in the past, and this time, as the reader knows, Montresor is going to fool Fortunato. Perhaps the greatest dramatic irony is that Fortunato is chasing after an enormous cask of gourmet wine which does not even exist.