An affair can hit at the very foundation of a relationship. It can never be easy to pick up the threads and move on. Trust is the main stay of any relationship, if there has been a breach of trust; it is not going to be easy getting it back. It may be possible that a relationship survives after an affair, but this can happen only if you are willing to work hard. 

I am not here to tell you that you can cheat at will and then come back and save your relationship. This should not happen. Swear off cheating. If you cheat habitually, these guidelines are going to be of no use to your relationship they will help only if you are willing to work hard towards it.

Bare truth: yes, you need to tell your partner that you cheated. Even if they don't know about it now, they may come to know of it later. So tell them now. You may think that this will hurt them, spare it and move on. But the fact remains that they might hurt later and then you will be accused of hiding it. This is the first step to rebuilding the lost trust. Tell your partner you cheated.

Carry your own cross: the easiest thing to do when you have an affair is to blame it on your partner. Yes, your partner may have been indirectly responsible for you having an affair, but ultimately it is you who cheated. You can't hope to rebuild a relationship by blaming your partner. Accept that you were responsible.

Apologize: you need to say you are sorry and mean it. Let your partner know that you really regret what happened and that it will not happen again. Don't try to explain your actions, just apologize and move on.

Give space: just because you said sorry, you can't expect your partner to forgive you. They are hurt and will need their space to come to terms with your unfaithfulness. You can't rush them into forgiving you.  They will forgive you when they are ready from their heart. Each time you push for forgiveness you will push them farther away.

Begin afresh: it is not going to be like the old times. The relationship will definitely be affected after an affair. You will need to start working on it as if it was new. You will need to build that trust all over again. This is not going to happen overnight, and you will need a lot of patience.