The details we can draw from the opening paragraph of this short story are that the narrator has already born a "thousand injuries" but did not seek revenge until he was insulted. Once he decided that revenge was the only answer, the two things he makes very clear are that he does not utter "a threat" and that he would carry out the revenge "at length."
Essentially what is said here is that the two most important things in carrying out a successful revenge were to take enough time doing it so that it was done with exactness (and perfection) and never to warn the victim in advance (by threat or otherwise). It would be a tragedy also, if the victim fails to know he is being victimized by the avenger.
Well, this is a very interesting question because some critics would say that you can't consider "The Cask of Amontillado" as a typical revenge story, because we as readers are unsure of how reliable Montresor is as a narrator, but leaving that behind, the first paragraph establishes the position of someone who feels (at least) that he has been grievously wronged by someone and wants to get his own back against him - the two classic ingredients of a revenge:
The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat. At length I would be avenged; this was a point definitively settled - but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
Montresor thus here expresses how insulted he has been by Fortunato, and also is defiant in his desire to see revenge visited upon Fortunato, but interestingly, in a way that lets Montresor get away with the crime and also express to Fortunato how much he has been insulted. Thus the stage is set for the rest of this chilling story...