The quarter-glass is the little side window at the back. People break them to get in, and they have to be replaced. We had to put one in today, and I looked on YouTube. This guy demonstrated how to do it, and he practically dismantled the whole door, so I thought this post might be helpful.
The main thing is that you have to move the pillar separating the main rear window from the quarter-glass, in order to get the new glass (in its rubber seals) in. You don't have to take the pillar out, just move it enough at the top end.
Roll down the main rear window all the way. Pull the rubber seals off near the pillar. The pillar is attached to the door-frame at the top by one or two phillips-head screws. These might be under or over the frame. There were two screws underneath in that YouTube video. On our car, there was just one screw, on top. One the screw was out, we could move the pillar enough to get the job done, without breaking anything.
Take your time. Make sure all the seals are fitted back properly, that the main window closes easily, and that the screw fits back in.
I suppose that on some models the pillar may not move enough, and then you are going to have to take down the whole main window, like our friend on YouTube. Just judge for yourself how far the pillar will move when freed at the top, without the use of excessive force. If you break it, don't blame me.