Most Helpful Girl
-admit you fucked up and show genuine remorse.
-don't give excuses as to WHY you cheated. That's beside the point and might just make things even worse as it may come off like you're attempting to justify your infidelity.
-let your partner know they mean the world to you and that you'er willing to do whatever it takes to help them rebuild the trust you broke.
Lastly- give them time. They won't start trusting you right away. They'll be super hurt and probably will never have absolute trust in you ever again. Which is a hard pill to swallow but such is life. Don't try to guilt-trip them into feeling like they HAVE to trust you. Be understanding of how they might forgive you, but will never forget. Proceed to show them not only that they can trust you, but that you're willing to face your wrongdoings head on rather than just trying to save face.
Most Helpful Guy
It's almost as hard for them to commit to loyalty as an alcoholic to not relapse but I've seen it happen.