You will need
  • the sincerity, desire to build relationships, a little patience and flowers.
You can ask for forgiveness theatrical wringing her hands, knocking with his head against the wall and stay in deep sorrow. This method is good in that case, when the quarrel was trifling. Such repentance will help to make the offended girl smiled.
Can be bought with care and attention, to do something that will be pleasant to hurt. Even if the gift and the help is rejected, don't despair, your actions for reconciliation are taken into account, only need a little patience.
Write a letter or SMS. In the epistolary genre to apologize easier when pre-thought-out text may start to sound unnatural. Your message will either re-read a few times that will work in your favor, or will delete without reading, which is also possible. In any case, after that there needs to be a dialogue, so you can demonstrate your sincerity.
In General conversation one of the good ways. Ideally, he should be calm, balanced and to help you resolve a conflict situation. Tell about your arguments, listen to the words of the opposite side. In that case if you feel that it is impossible to find out the truth in the dispute, but do not want to be in a state of quarreling, just say that everyone remains at the opinion. Don't settle for the mind, it will generate new conflicts.
You can just go to the girl, to admit their mistakes, if it is appropriate, hug her, listen to all what people think about you, show the depth and sincerity of his repentance. Correct their mistakes, is it insists, offended.
You can demonstrate remorse and penitential silence, sad eyes, heavy sighs. People who are not able to ask for forgiveness, experiencing everything inside, it's hard. Sometimes you have to comfort them, to say that nothing terrible happened.
Also you can cheat and pretend to be offended himself, it will cause a confrontation between the characters. The first to make concessions to the one who is softer. But on the other hand in such a confrontation can take years, during which people in General can forget that it is not shared.