Dr. Josh offers his "shrinkage" on how to really say your sorry. Often this comes after an affair has been discovered. However it can really apply to any major relationship betrayal. A summary is below. Listen to Dr. Josh discussing the topic in this podcast from The Web Radio Show.
Dr. Josh's Shrinkage: 5 Steps For Apologies After A Major Betrayal
Step 1: Understand what you are apologizing for
Be clear. What are you apologizing for specifically. Think about it. Saying your sorry is important but not enough.
Step 2: Accept responsibility.
No "but" allowed. You did it, it's your fault. Stop there.
Step 3: Offer alternatives.
Show that you really thought about this. What should you have done differently? How should you have handled this in a different way. Saying "I shouldn't have cheated" is not enough.
Step 4: Abolish expectations.
This is about your apology – no expectations for your partner to do anything, say anything or forgive you.
Step 5: Say, “I’m sorry.”
It's critical that they hear those words from you.
(source: http://www.huffingtonpost.com/…/how-to-apologize-affair_n_3…)