When your friend apologizes, the correct thing to do is verbally indicate that you accept their apology and then let the issue go.
Sounds simple enough, right? So why is it so difficult for people to do? Sometimes people are not ready to forgive someone, so they put off accepting their friend's apology. Or the reason may be more vindictive: they want to make their friend suffer a bit more for hurting them. While both of these situations are understandable, they aren't the kind thing to do.
Accepting an Apology Is the First Step Toward Forgiveness
It is best to accept the apology you're given, provided it is genuine and not a so-called non-apology. Your acceptance is the first step toward forgiveness. This means you'll still feel hurt but your will be on your way to letting it all go. With forgiveness, the decision to forgive comes before the feeling of complete forgiveness, so it's natural not to be "over it" when you accept your friend's apology. Trust that when you say you forgive your friend your feelings will come shortly after.
When You're Not Ready to Forgive
Revenge is never the answer. So if you still feel that you need to make your friend suffer after they have apologized, take a step back and consider the consequences of putting off the acceptance of their apology. They may think you will never forgive them and choose to pull away from the friendship altogether. No one likes to be reminded of the times they have messed up, so if you're not ready to forgive, instead say something like:
I appreciate your apology and I accept it. It means a lot to me. I'm not quite ready to forgive, but I want to be, so I hope you'll be patient with me.
Once you reach this step, it is important to not continually bring up the issue. Instead, work to get through it so you two can be friends again. Don't insist that your friend apologize over and over or hold it against them in future af. This only damages your friendship and will make your friend less likely to apologize next time.
Embracing Acceptance When Your Friend Apologizes
Truly accepting an apology means that you have thought it through, acknowledge that your friend made a mistake, and embrace the fact that your pal is sorry. While you might still be a bit angry, you are on your way to letting go of that in favor of a solid friendship once again. Saying that you accept your friend's apology means that you are willing to put an end to the argument in such a way that it will not continue to be an issue going forward.
A good way to acknowledge this is to say something like:
"We all make mistakes. I accept your apology."
"After thinking it through, I realize this was just a misunderstanding and that you didn't mean to hurt me. I accept your apology."
Your friend will remember how you were able to accept their apology and when it's your turn to be forgiven, they'll be more likely to accept your apology quickly and let it go.