First, we pulled off all of the baseboard molding. This would allow us to get right up to the edge of the floor with the sanders and floor finish. Conveniently, we also decided that we didn't like the molding very much so there was no point in trying to preserve it to reattach when the job was done. It was much easier to remove without caring whether we splintered or broke pieces of it.
Once the molding was no longer hiding the edge of the flooring, we discovered such charming details as this:
This method of securing the flooring was surprisingly common in our rooms. While the original carpenters might have thought that this was a good way to secure the flooring, it wasn't going to fly with us. So out came all of those nails.
We also had to remove nails that hadn't been driven all the way into the flooring, or had loosened over the years. The easy thing to do would have been to sink the nail in the rest of the way. Unfortunately, the carpenters had used some ill-advised nails with inappropriately large heads:
So, once all these nails were removed, we had a lot of floor boards that were no longer actually attached to the floor. P went around, taping on all of the boards bordering walls with his hammer, and whenever he saw any movement, he drilled a pilot hole and then drove in a new nail. (The pilot holes and better nails prevented any new cracks in the floor boards.)