Crazy though he may be, Montresor certainly uses his wits in his revenge on Fortunato. First, he hides his true feelings in order to lure Montresor into a false sense of security; he doesn't let on that he has experienced any change of feelings.
It must be understood that neither by word nor deed had I given Fortunato cause to doubt my good will. I continued, as was my wont, to smile in his face, and he did not perceive that my smile now was at the thought of his immolation.
Montresor also chooses his bait well. He picks something he knows Fortunato cannot refuse: the chance to inspect a very valuable old wine—a cask of Amontillado.
He also is very clever in recognizing his friend's vice: his pride. He knows that if he appears to give preference to another wine expert's advice, Fortunato will be anxious to prove himself and prepared to go anywhere and drop anything to do so.
"Luchresi cannot tell Amontillado from Sherry."
"And yet some fools will have it that his taste is a match for your own."
"Come, let us go."
He also chooses carnival time to get his revenge, when the streets are crowded, people are less attentive, his servants are out making merry, and he himself can wear a disguise: "a mask of black silk and ... a roquelaire." It also helps ensure that Fortunato isn't thinking clearly—he's already drunk, since his eyes betray "the rheum of intoxication." He also cleverly works to keep his friend that way: "A draught of this Medoc will defend us from the damps."
What's more, he has clearly prepared the scene; he has the chains ready so that it is "the work of a few seconds" to loop them around Fortunato and lock him in.