I was cheated upon in my last relationship, a 6-yr relationship that was co-residential for the last 3. After I discovered the cheating, my ex did just about everything that a truly penitent cheater must NEVER do. For the record, they are:

1) do NOT minimize or rationalize what you did or try to turn the tables on the person you've wronged. There will come a time when the two of you can assess mutual mistakes that led to the A, but now is NOT the time. You did it, now you take full responsibility. Anything less will be ruinous.

2) utterly and completely cut off all contact with the OP, and do so in a way that is as transparent as possible to your spouse. Your spouse will be very suspicious for a few months, and if you have any further contact of any sort at all, no matter how innocent in your mind, your spouse will discover it and that discovery will further devastate him/her, and probably kill any chance at reconciliation.

3) if you compounded the problem by telling a friend or friends that you were having the affair, and those friends implicitly conspired with you by not telling your spouse, you'll need to exclude those friends from your social sphere until such time, if ever, that your spouse can bear their company again. It is altogether likely that your spouse will have no use whatsoever for such "friends" ever again. If that's unpleasant for you, too bad--you did this, and that's part of the consequences.

4) if your work or academic program thrusts you into the OP's presence, you're in a real jam. If your spouse asks or implies that he/she would be much more comfortable if you'd not see the OP even in those circumstances, you're going to have to change employer and/or academic program. If that seems excessive, too bad--you did this, and that's part of the consequences.

5) now is NOT the time to insist upon the sanctity of your right to privacy. After all, you abused that privacy by sneaking around with the OP. If your spouse has questions about exactly what happened and where and how and how often, answer them honestly. He/she has a justifiable need to feel assured that you have no more secrets and are willing to come clean, and however uncomfortable that might be for you, you're going to have to step up and comply.

6) do NOT tell any more lies of any kind. Especially do NOT tell lies if/when your spouse confronts you about the A. Fess up and take your lumps. If you do lie, and the lies are found out, it will be vastly more difficult for your spouse to regain trust in you, and sometimes the chain of lies that you tell in attempting to conceal the A will do as much harm (it can't do more) than the A itself. ESPECIALLY do not employ false outrage or indignation at your spouse's suspicions or questions--that will be utterly ruinous once the A is discovered. He/she will feel that you tried not only to betray him/her but to make a fool of him after the fact.

The best policy, obviously, is not to get into this sort of horrible jam in the first place. But if you went ahead and did it, and you sincerely want a reconciliation, you're going to have to follow these rules unstintingly, at least for a while. That's just the way it is after you've betrayed the trust of someone who loves you, and if that's a tough gig, too bad--you did this to both of you. Period.