You would either accept their apology for whatever the reason or you can choose not to accept it. You have the choice.
Always try to accept any apology you think is sincere. That doesn't mean a relationship automatically returns to it's previous status. If there is time needed to heal , or trust to be re-earned, the person who transgressed must be made to understand that.
In person!
just say i am sorry for what ever you did
say sorry and dont do it again
Apologize for what you did. If they still are mad, then they are not a good friend
Te pido disculpas. OR Perdóname.
You may say 'sumimasen' to apologize if something you are doing is inconveniencing someone. (In this way, it is similar to 'Excuse me.' If you bump into someone, you can say 'sumimasen' to apologize. It can also carry the meaning of 'thank you;' you may say it, for example, if someone serves you something.) Other methods of apologizing are; 'Gomennasai,' 'gomen ne,' and the very polite 'moushi wake arimasen [deshita].' Meaning "I have excuse," it can be used to apologize for bigger transgressions.
You don't, or you say " Sorry, but why am I apologising?"
I know I let you down by telling you something that was not the truth and I apologize for that. I will never do that again and want to know how I can make it up to you and earn your trust back.
Well if you did something wrong to a person, yes please apologize. No one has ever choked to death from swallowing pride.
To apologize is to say sorry for something. To ask forgiveness is to ask someone to forgive you and let you go even if you have commited a crime or sin.
Just ignore them completely and seem like life without them is better.. Then they will see how happy you are without them and want to become friends again so they apologize.
to / forI want to apologize to youI want to apologize for last my behaviour last night