Learning how to initiate conversations is hard, especially for a WS. Most WS's would prefer to NOT talk about the affair, because it only hurts us and reminds us of how shitty a thing we did and how guilty we feel. We also tend to tell ourselves that bringing it up will only serve to hurt our BS's more, and that's true to some degree.
The thing is, our BS's NEED to talk about it, in order to process what happened. Yes, it hurts them to talk about it, but it also helps them more than it hurts, because it allows all that sadness and anger and pain to release and to process. That much, they can do on their own. They can initiate their own conversations.
What's missing for most BS's is YOUR part of the story, all the things they don't know. Early on, this is often the Who/What/Where kind of questions, and if you are willing to be honest and open, this part can move pretty quickly. Just remember that they were not there for most of the affair, so to them, this is all new, a puzzle without most of the pieces, and so they are relying on you (the person who betrayed and lied to them in the first place) to fill in those pieces. It helps them a LOT to not have to drag that info out of you. That's one of the things you can help with.
Once the Who/What/Where is mostly filled in, then comes the much harder questions of How/Why? Again, the WS temptation is to rug sweep on this. We often don't want to admit to ourselves or to our spouses how bad things got, how we really felt at the time, the fine details about how we ended up betraying them, making them feel kicked to the curb and discarded, and how we took to some other (usually much inferior) person to fill those needs.
Again, your BS needs this to heal. And quite frankly, so do you. Most of us WS's tell ourselves a lot of lies and justifications and other bullshit to allow this to happen. But why? Was getting a piece of tail worth risking your entire marriage over? Usually not. Most of the time, the affair is a symptom, not the problem. (Well, speaking for the WS I mean). The real problem is within you. What need do you have that wasn't getting filled? Did you feel unloved, unwanted, unsatisfied? Did you end up blaming your spouse for this? Did you feel that you deserved more, deserved some happiness in your life?
As you talk and start to dig, you might be surprised to find out how much of that train of thought was a cover-up for things missing in YOU. Was your spouse really unloving or was it just a reflection of how you were treating them? If they were being loving, why was that not enough? Is it because you didn't love yourself enough and thought you actually deserved someone less, someone as miserable as you were?
Don't be afraid to open up. I can't gaurantee what result will come. They will probably be mad and hurt, that's true. But the likelyhood of them processing that pain and respecting that you were open and honest and owning it, will go a long way towards restoring trust and respect.