According to Montresor, one requirement is that the person seeking revenge must not allow his desire for revenge to ruin his life. If you want revenge so badly that you obsess about it, or if you can't function on a day-to-day basis, then revenge cannot be successful. You must carefully plan your revenge, carry it out, and go on with your life.
Montresor's second requirement for successful revenge is to tell the person you want revenge against that you are the one who is angry with him. In other words, if you're going to punish someone for hurting you, let him know when you punish him that you are responsible for the punishment.
Don't plan a sneak attack, but be there to see it happen. Some scholars have felt that Montresor is also saying that you must tell the person what he has done specifically, but not all agree that this is what he means.
I also discuss with my students whether Montresor has met his two requirements for successful revenge. I don't believe he fulfills the first requirement because he is still talking about the revenge against Fortunato 50 years later. Has he been obsessing all these years about it? If so, he failed his first requirement. As for the second requirement, he lets Fortunato know he is angry with him for some unknown insult, but he doesn't tell Fortunato specifically what he is angry about. My students always have a good discussion whether Montresor has fulfilled his second requirement also. It all depends on what you think Montresor is saying in his second requirement.
Montressor tells us very early in the story what is needed for a wrong to be redressed in his eyes. He says, "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."
Therefore, to be redressed, retribution (vengeance) is necessary, and taking personal responsibility for hurting the one that hurt you (and letting him or her know it).