"A soft word turns away wrath," as the saying goes. And this is particularly true when someone is angry because you have insulted her. Include an apology along with your gentle words and you just might salvage a relationship. At the very least, you'll be working to re-establish a climate of respect rather than animosity.
Think about the incident for which you are apologizing. Consider your words and the effect they may have had on the person. Empathize with the person you hurt if at all possible. A sincere apology will be more meaningful than one that is forced.
Plan the words you intend to say to the person. You don't have to recite the exact words you come up with, but having an idea of what you're going to say will help to prevent you from sticking your foot in your mouth when he is standing there looking at you with a skeptical look on his face.
Look the person in the eye and use a gentle tone of voice to convey your apology. Tell her you are sorry. Keep your words spare. Psychologist Tamar Chansky, in a July 2012 article in "Psychology Today," notes that there is no need to apologize for your entire existence. Saying that you're an awful person is likely to make the other person feel worse, not better.
Acknowledge that you know your actions may have caused hurt. You might say something like, "I realize that when I said those mean words, you may have felt angry and embarrassed." Note that repeating the insult is not necessary when making your apology.
Accept responsibility for your words, says author Beverly Engel in an article for the University of Massachusetts Amherst. Don't dilute your apology by saying, "I wouldn't have said that if you hadn't laughed at me, though." Blaming an insult on drunkenness, another person or any other circumstances makes you appear immature and incapable of managing your behavior.
Make reparations. While you can't take back an insult, you can give the person you offended your word that it won't happen again. Once you've promised to respect the person with your language, stick to your word.
Move on with your life. After you've hurt someone's feelings, it's tempting to sit and ruminate over what you could have done differently and wonder if your actions will have a permanent negative effect on your relationship. Don't give in to this temptation. After you apologize, put the incident to rest.