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!