The first thing you need to do is swear off affair relationships. This is not a guide on how to cheat on your partner. If you're going to continue to cheat, then these guidelines will not be of much help to you. If you're willing to do the work, then these tips will help you repair your relationship.
The first thing you to need to do is admit your affair. Relationships are built on trust, and you can't have trust when you're lying to the other person. Not telling them is lying, a lie of omission. You need to tell them if they don't know, even though it is going to hurt.
Aside from general honesty, which is always a virtue, there is a practical side to this as well. If they don't know, they will find out, and it's better that you take the bullet now rather than add to the pain when they do find out. If you try to keep it a secret, you're going to torpedo the relationship.
The next thing you need to do is to take the blame. You may feel that your partner did something to drive you to cheat. We also all have natural tendency to rationalize our behavior, to explain ourselves by coming up with an excuse. But the reality is that it is you that cheated, you that the affair. Relationships aren't built by blaming your partner for your mistakes. Take the blame and move on.
Then you need to apologize. What you're looking for here is a complete admission and a sincere apology. You need to make sure that they know that you are truly repentant and regret what you did. Don't try to explain, just let them know how you feel.
Once you've done that, you need to give them some space. They are going to react, they are going to be hurt, and you can't push them into forgiving you any faster than they are going to already. Be there for them, but make sure that you don't push. They will be ready when they are ready, and if you try to push the issue then you are only going to succeed in pushing them further away.
After an affair, relationships are going to be different. The best thing you can do is to look at it as if you are starting the relationship all over again. You're going to need to win back their trust, and this is a process that is going to take some time.
Fortunately, there are resources available to you to help you repair the relationship. It may be hard to admit to yourself that you need help, but using one of the systems can be the best relationship move you'll ever make.
Read more in The Magic Of Making Up