“To forgive someone about what he/she did to you” and “to apologize to someone about anything wrong that's been done” are our normal practices in order to learn how to be at peace and be careful of our behaviours toward others. These actions lead us to the non-existence of the consequences for sins or cancellation of penalties for all sins we created in the past.
At the beginning of most group gatherings and often throughout the day, there are various forms of prayers for forgiveness given. The purpose of these prayers is to provide a way to release thoughts or feelings that we perceive to be unhelpful. It is also used to clear any bad feelings or conflict that may arise between two or more people.
What we normally say is something like this; “I sincerely perform my apology to everyone supposing that I have intentionally or unintentionally offended them by words, thoughts, or any actions both in present and past lives I have lived. I beg your forgiveness from the depth of my heart.” And “I would like to forgive those who have done any wrong to me. I am so pleased to extend my virtues and good qualities to all beings and wish all beings peace and happiness.”