Poe uses many Gothic elements to create this masterpiece of the macabre.
First, he uses a superb narrator, Montressor, who shows vast intelligence, cunning, and manipulation. But, as the story unfolds, we realize he is not only unreliable, but quite mad. His plan of revenge is clearly premeditated, but he never divulges the offense Fortunado committed against him and his family, thus confounding the mystery. At the end, after we realize Fortunado's murder occurred 50 years ago, we gasp at how fresh the tale how been told by the murderer. He relishes it still as an old man, showing no guilt.
Second, Poe adds suspense through setting. The ancient city, Mardi Gras, the catacombs, the niter covering the walls, the niche used for Fortunado's grave. Most Gothic horror stories are set in haunted houses; here, we have an underground network of them: the old burial grounds instill fear in the soul of any in Christendom.
His primary device used to create suspense is foreshadowing. Montressor reveals his coat of arms to Fortunado, the snake biting the heal that steps on it--a clear symbol of revenge. He shows the trowel to him and gives him the phony Masonic gesture. And then there's the amontillado, the greatest red herring in literature.
Because this is a frame story, the ending of inner story of revenge is never in doubt. We know Fortundo is being lured to his doom. But, the motive for the murder is never given, so the outer story of confession seems uncharacteristically hollow and open-ended. Gothic narrators usually relish in how fitting the revenge is to the original crime. Montressor may be so mad that there never was one. To me, the ending of the outside story is very much in doubt.
One technique that Poe uses is letting the reader know right off the bat, that Montresor was out for revenge, and that he would punish with "impunity". This bit of foreshadowing is ominous, and immediately sets up a sense of suspense; we are left wondering, the entire time, just exactly if and how he is going to get that revenge. So, the use of allusion and foreshadowing right of the bat sets up the suspense.
Another way that the suspense is heightened is through the setting and environment. Montresor leads Fortunado down through the winding catacombs; this maze-like configuration only serves to confuse us, to heighten our apprehension and to set us on edge. We wonder when it will end. If he was just in the city, on a walk, going to a room or an alley, it would not be as suspenseful. These are normal environments that we are familiar with, that aren't underground, cold, damp, and filled with the bones of dead people. The catacombs are also winding like a maze or labyrinth, which are created to disorientate people. So, the setting itself is like a horror film, winding through endless, dark, corpse-filled mazes with no end in sight. That environment serves to increase the suspense.
One other way the suspense is heightened is Montresor's obvious mocking and manipulation of Fortunado. He "insists" that they turn back at several occasions, feigning concern for Fortunado's cough. He plays the role of caring and loving friend, all in an attempt to oust Fortunado's ride and sense of manliness. We know that the man is merely egging him on, which makes it all the more infuriating. The character of Montresor himself--his malice, his sarcasm, his manipulation of the weaker Fortunado--all lends itself to the creation of a pretty creepy villian, which increases the suspense.
Then, once Montresor's plan becomes obvious, that he is indeed going to wall Fortunado in and leave him there to die, the suspense is at its height, and Poe uses Fortunado's naive misunderstanding of what is going on, then his dawning terror, and eventual silence to create concern and kinship with the unfortunate Fortunado. We long for his escape, we rally to his cause, and that creates more tension because we are relating to the character, and hoping that Montresor won't succeed.
These techniques, in addition to a simply good storyline and plot, all add heightened suspense throughout the story. I hope that those thoughts help a bit; good luck!