It seems to me that much of the advice on here is either on one extreme or another: either "throw cell records in their face" or "accuse", or "just make myself pretty and hope he comes back to me" kind of stuff.
I may be old-fashioned, but I did neither. When I had proof of my wife's infidelity, I simply said "I know about you and ______, and it has to stop. You're being disrespectful to me, to our marriage, and to our family, and I won't tolerate it. You have a decision to make, and I won't wait forever for you to make it."
And that was my approach. She fought like hell for 2-3 months, and I ultimately had to serve her with divorce papers, but she ended the affair, came clean with her parents and our adult daughters, and finally came to me in tears begging me to take her back.
Most people focus entirely on the efficacy of what will "work" to get the wayward spouse back. And I also think confrontation and exposure works on that front, but not always. But I also think there's another consideration, and that is the self-respect of the betrayed spouse! What is your personal integrity, and how can you live with YOURSELF if you simply sit back and tolerate your spouse's affair? How much respect will THEY then have for YOU that you tolerated it?
They may scream like a demon with holy water poured on them, but later, they will see how you fought for them and for your marriage, and your kids will see how you did the same.