Step 2: Accept responsibility.
When it comes time to offer an apology, you must, above all, be clear about what you have done. Be absolutely certain not to shirk responsibility by sharing the blame with anyone or anything else. Apologizing is not saying, "It never would have happened if I hadn't been hanging out with my sister," or "The captain shouldn't have assigned me a female partner." In particular, be careful to avoid labeling your spouse as responsible, for example, with words like: "If only I had been getting more love from you, I wouldn't have looked elsewhere." Your behavior is your responsibility and no one else's. You'll know you're on the right track when no one offers any disagreement about what you are apologizing for.
People sometimes try to decrease their own responsibility by adding "if" to their statement about the other person's reaction. Saying "I'm sorry if what I did hurt your feelings" is very different from saying "I'm sorry for what I did, and I know it caused you pain." The "if" statement tells the person that you have remorse about the outcome, not about your actions. Don't do that.
Step 3: Offer alternatives.
You've probably heard the advice to stay away from the "coulda, woulda, shoulda" attitude toward life. Well, here's a place where this is exactly the attitude you need. A hearty dose of "I should have told you that I was going out to lunch with her," or "I wish had not shared my problems with him" tells your partner that you understand there "coulda" been a better way of handling things, and gives hope that you will make better choices in the future.
Step 4: Abolish expectations.
Another aspect of a genuine apology is to offer it without expectation to get something back. This isn't a proposition of "I'll say what I did wrong so you will tell me what you did wrong," or even "I'll say I'm sorry if you say you'll forgive me." Your sole goal should be to make sure your partner hears you. It's certainly okay to offer the hope that your partner will accept the apology, but you cannot make that a condition for offering it.
Step 5: Say, "I'm sorry."
You may be thinking that you are very, very sorry. You may have admitted to all your wrong doings. You may have asked for forgiveness, and you may have promised never to do it again. But your partner may still turn to you and say "You never said you were sorry." Don't forget to say you're sorry!
Studies about gender differences reveal that women tend to offer spontaneous apologies more than men do. Women are more likely to perceive things they have done as requiring the offer of apology, but men tend to see real and imagined wrongs as not deserving an apology, because they "weren't that big of a deal." In the case of affairs, there is no room for gender differences: saying "I'm sorry" is a necessity.
Not every affair gets splashed across international headlines, but mistakes do happen in everyone's lives. That's what apologies are for. Having an affair is a big mistake, and it healing requires a genuine apology. Then the rebuilding can begin.