Okay so I'm coming from this at the opposite side. When hubby and I started this it started badly. In other words, I was neck deep in the asshattery of lying and trying to cover those lies. I can give you all the reasons, embarrassment, NRE, blah blah blah. The truth is, at the core of it, I knew that feeling I needed to lie about it, meant it was a problem. So I won't go over all the excuses she is probably feeding herself.
What I will say is that we got through it. How? Transparency. That meant if hubby wanted to read my emails, he did, my chat logs, check my phone. Whatever. Oh sure there were times I was still embarrassed, but I knew that I put myself in that position. Slowly, it got to the point where I could say, "Well this is a little more private I'm not sure XYZ would want to share it, but yes that's who I'm talking to." And that was enough. That took time though.
I get she may be feeling embarrassed and want to apologize and clean slate it. Sadly, life doesn't work that way. Oh and as far as the years before the lying? Hubby and I have been married more than 15 years. So this wasn't a newlywed, newbie mistake. So it was something I had to understand and hubby has mentioned that it wasn't the talking with someone else that hurt, it was the lying. We have talked to many other people that came to poly through cheating and the main thing we say is that the lying is like destroying the foundation of a house. Sure you can try and ignore it and keep living in the house but it won't last long and it's not safe or good. You need to rebuild that foundation. Which meant for us not just promising to be honest, but showing it by allowing him to see and read and hear and know everything I did. Even sitting next to me while I was emailing or IMng the other person(s).
After me screwing up there were two simple rules really:
Rule One: Transparency, he wants to know, he gets to. He wants to see, he gets to. I'm earning back trust by having nothing to hide.
Rule Two: I hurt him, as much as he needed to talk about it, I needed to listen. Even if reminders of my asshattery made me cringe horribly.
Me: Late 30s pansexual poly. DH: My husband of 17 yrs and father of children. DC: LDR of +2 year