Admit it. To yourself, then to others. 

The first and hardest step. We all have inherently large egos considering our inevitable placement at the very center of our respective universes. Reality exists by us and other people exist through us. This isn't an inherently wrong proclivity— there is no conceivable way to make sense of the world if not by way of prioritizing our own perspectives. Yet, we must admit that other perspectives exist, just as other people exist, and those other perspectives, though not placed at the convenient center of our universe, can be just as if not more valid for that very reason.

Apologize for that which you are sorry, don’t apologize for that which you are not.

The latter is crucial. If you apologize for more than you mean, the true apology bears little weight. Diluting an apology is like rejecting a compliment. Both reactions present issues of insincerity rooted in our personal discomfort. By reacting insincerely, we transmit discomfort to the other person, making them unsure of how to digest our true intentions. We must learn how to rightly give and how to rightly accept.

Do not dwell.

Do all you can to rectify the situation and there will be no reason to allow your guilt to linger. Know what you are responsible for, your actions and your reactions, and then enforce your boundaries. Once you have given the apology owed, do not allow yourself to feel (or anyone to make you feel) as though you owe anything more.

Allow your mistakes to inform your future success. 

If you realize too late—to the point where an apology would be futile— forgive yourself. Establish a conscious effort to do, to be, better.