So far the two stories we've written together have gone similarly. We've talked out the story and its structure and characters together first. Then we've sat down in the same room and taken turns writing chunks of prose.
This one is a fairly section-based story, so we would each take a section and go with it, appealing to the other if we were grasping for something and couldn't quite reach it. The other story we've written together was much less divided, so we would just write until we reached a point where we didn't feel like going on and would pass it off to the other one. Then we each did read-throughs and talked about the revisions together until we were satisfied.