Someone who is asking for forgiveness must specify his offense. If the wronged party was not aware of the offense, the person requesting forgiveness must confess it to him and ask his forgiveness (Baḥ). However, if he knows that detailing the sin will cause the wronged party pain and embarrassment, it is better that he not specify it (MA; MB 606:3). He should also do his very best to neutralize the impact of the negative things he said. He should make a point of speaking highly of this person to counteract the earlier disparaging things which he said.
Le-khatḥila, one who has hurt another should ask forgiveness himself. However, if he is too ashamed, or if he thinks that the injured party is more likely to be receptive to someone else, he should ask forgiveness through a middleman (Mateh Ephraim 606:1; MB ad loc. 2).
If the injured party initially refuses to be placated, the penitent should approach him in the company of three people and request forgiveness in front of them. If forgiveness is again withheld, he should try again (with three people). If it is still withheld, he should try yet again (with three people). If the injured party still refuses to forgive, the original offender does not have to do anything further. The unforgiving party is now the sinner. However, if the person hurt was his Torah teacher (even if not his primary one), he should keep going back, even a thousand times, until he attains forgiveness (Yoma 87a; MT Laws of Repentance 2:9; MB 606:7; BHL ad loc.).
The injured party should not be cruel and refuse to forgive. As our Sages state, “If one foregoes injustice [done against him], heaven will forego punishment due to him” (Rosh Ha-shana 17a). If he does not grant forgiveness, his sins will not be forgiven in heaven. However, if his intention is to help the offender by teaching him to be more careful in the future, our Sages allow him to make the sinner request forgiveness several times. Even when the offended party officially refuses to grant forgiveness, in his heart he should immediately stop hating or being angry at the person who hurt him (Rema 606:1; MB ad loc. 9).
If one is concerned that if he forgives, the offender will repeat his offense, he is not required to forgive. Similarly, if one spoke badly of another and seriously damaged his reputation, the injured party is not required to forgive the offender, since some people will have heard the slander and not the retraction. Even so, if the offender truly regrets his action, publicly apologizes, retracts what he said, and does his best to undo the damage he caused, it is proper for a pious and humble person to forgive him. (See Rema 606:1; MB ad loc. 11.)
If the injured party has died, the person who hurt him must bring ten people to his graveside, specify his sin, and confess that he sinned against the God of Israel and this individual. They then declare three times, “You are forgiven” (Yoma 87b; SA 606:2; MB ad loc. 15).
Some people ask forgiveness from all their friends and acquaintances before Yom Kippur. However, this practice is almost meaningless. People fool themselves into thinking that because they are so careful to ask forgiveness from all their friends, this makes them pious. In fact, though, they are acting wickedly, because they are not asking forgiveness from the people they actually hurt. Rather, the main idea is to do soul-searching before Yom Kippur and recall those whom one may have truly hurt. He should then request forgiveness from them (Shlah, Masekhet Rosh Ha-shana, Derekh Ḥayim §151).