We all make mistakes, and some of them are bigger than others. No one can deny the fact that cheating on a spouse or a committed partner is a big one. So what do you do once the damage is done, and better still, how do you deal with the problem and fix the situation … and, furthermore, can it be fixed?
Why?
The first thing to understand is that cheating often signifies that there is something wrong with, or missing from your marriage/relationship. You will be unable to go forward until you analyse what the problem is.
Communicate
If you were caught cheating on him, he'll be very angry, and will most likely ask many detailed questions. These are going to be hard to answer ... but be honest. If you shut down now and refuse to answer further mistrust can develop.
In order to fix it, you're going to have to reprove your love, which means dealing with his lack of trust for you over a LONG period of time. Be willing to call him if you're going to be late, and if he asks you to be in touch, then BE in touch. Furthermore, don't give him reasons not to trust you. If he asks you to come home early ... come home early.
Understand that, in situations like this, emotions will run deep and strong
By your actions you've torn away a piece of his heart and that scar, like any other, can last for the rest of his life. That doesn't mean you can't salvage the relationship. Explain to him that there is no excuse for your actions and that cheating was an inappropriate solution. Let him know with what aspects of the relationship you're not happy and consider counselling.
Apologise
Make sure you deliver a complete and proper apology to your partner. This CAN be the first step in the long road to forgiveness. Don't place blame or try to justify your actions. Nothing short of admitting fault, apologising, and communicating about the problem, will help the situation.
Cut off communication completely with the third party
Obviously your partner isn't the only one involved in this now that you've cheated. You've taken an outsider into your relationship as well. You need to contact the other person, and explain to them that your actions were wrong, and that you need to repair your relationship with your partner. To do this, you will need to cut off all ties to and communication with the third party.
Patience
Don't set a time limit for how long your partner is "allowed" to remain hurt or angry. You set this process in motion so you must be prepared to deal with the mess your selfishness has left behind. Remember, it takes a moment to break down trust and a lifetime to rebuild it.
He will continue to hurt over your actions so make it up to him. He's going to feel insecure and not trusting of anything you say or do. You need to prove that you are there for him, that you are sorry for what happened, and that you still love him.
Your decision
Whatever you decide, do what you feel is fundamentally right for both you and your partner.