With regards to asking forgiveness there are special halachot in the code of Jewish law specifically with regards to yom kippur yet in truth this is applicable all year long.
The halacha is that if one sinned to his friend ,hurt him physically or emotionally or mistakenly thought of him something bad, although he compensated him of the loss he caused him he is still
not forgiven until he actually asks him for forgiveness (and this can be at any time).
[1]
In the Talmud we find that rabbi Eliezer says that yom kippur does not atone for sins in between man and his friend until one obtains forgiveness from his friend.
This means to say that it is not sufficient just to ask for forgiveness it is very important that the request will be accepted, that the friend will actually forgive.
The halacha is that one is to ask forgiveness to one who is upset with him although in truth there was no reason for him to get offended and even if the one who got offended responded in a non- honoring manner.
One who knows that the one who offended him has totally forgiven him is nonetheless according to many halachic authorities ask him for forgiveness as he is required to break himself through asking for forgiveness.
[2]
One is to ask forgiveness face to face yet if that does not work as he is too embarrassed or being that can’t meet physically then he can ask with a messenger (shliach) in certain situations this will be the preferred way of communication.
[3]
The one who is asked forgiveness should not be mean or strict rather follow the way of the Israelites and forgive full heartedly easily in a manner that he is willing to pray for the other and as the Maimonides writes whoever does so quickly the rabbis have much nachas from him.
[4]
Yet the one who was hurt, offended, does not need to forgive until the one who hurt him stops to hurt offend him or if there is a financial dispute until the monetary issue is resolved and only after all the issues are taken care then go ahead and forgive,
So to one can hold back the forgiveness when they’re intention is for the sake of the one who asked forgiveness in order that he should internalize how serious what he did was, and so to in a situation were it is evident that although he is asking forgiveness but it seems evident that he intends to do the bad action again.
[5]
So, it is important to ask forgiveness full heartedly and once that happens one is to full heartedly forgive.
If one asked forgiveness yet he wasn’t redressed he is to ask pardon again in a different manner if that doesn’t work he should try a third time in a different manner, the Shulchan aruch harav writes that each time he should take three people with him.
[6]
If he tried three times and it did not work, he should then proclaim before ten people that he tried three times to achieve forgiveness and yet the other side did not forgive (that way people will know he tried) and that is sufficient.
in any case when it Is difficult one should appoint a arbitrator to go in between them and make peace and definitely when we make peace with our brethren we merit to the special blessing from g-d ברכינו אבינו כולנו כאחד
[1] ספר מצות הלבבות הל’ נו”נ י”ט.
[2] פלא יועץ ערך תשובה.(אבל ראה שו”ת דבר יהושוע ח”ה סי’ ב’ שמעיקר הדין ל”צ).
[3] משנ”ב סי’ תר”ו סק”ב.
[4] רמב”ם חו”מ פ”ה ה”י.
[5] שולחן ערוך הרב סי’ תר”ו ס”ד חיי אדם תפילה זכה, משנ”ב סי’ תר”ו.
[6] שולחן ערוך הרב או”ח סי’ תר”ו ס”א.
