People are complicated. Every single one of us is completely unique. Conflicts arise between us, as divergent as the things that make us who we are: differences of opinions, stress-related strain, failing to see eye-to-eye and even interpersonal competition. Whether you are childhood friends or married for decades, unfortunately, hurting someone at a point is inevitable. The good news is that it does not necessarily have to mean the end of the relationship, as long as you respectfully and humbly offer amends.
Admit to yourself that what you did was hurtful. Try putting yourself in the other person's shoes. Acknowledge the fact that what you did was hurtful and take personal responsibility for your actions. Do not blame the other person for being upset.
Contact the person and admit that you caused a wrongdoing. Request a chance to apologize and a convenient time to meet and discuss what happened. Meet somewhere that feels comfortable for the hurt person. Depending on how severely you hurt the other person, she may want to meet in a private or neutral setting.
Conduct a face-to-face apology. Apologize sincerely for your actions without justifying or excusing your actions. Admit honestly that what you did was wrong and hurtful.
Give the person time and space for healing. Have empathy for the time it takes for her to heal. Give her space --- and her own unique pace --- to forgive you. Let her decide when it is time to move forward.
Let the person contact you or tell you that it is OK to start rebuilding the relationship. Depending on your relationship, this might be a phone call, an email, a brief conversation, or even subtle body language. Offer suggestions to the person for repairing your relationship.
Approach selflessly the relationship. Commit to both yourself and the other person not to repeat the same mistake. Follow through with your commitment of not hurting the person again.
Accept that you may never earn her forgiveness. Being in a relationship is about respecting another person's feelings. Understand that what you did might be too difficult for the person to forgive. Respect her decision and accept the situation if the relationship ends. Learn from the mistake.