Get Prepared - Ideas on How to Insulate the Shaft
Take you level and hold it's edge up against each stud, from the top header to the bottom header, all the way around the shaft. It should lay fairly flat without any serious gaps between the studs and the level. If there are, you either picked some dog crooked studs or something isn't plumb. Fix it before you continue.
Insulating The Shaft
You don't want condensation to develop in the shaft. To prevent this, you'll want to insulate it. If your ceiling and roof are already insulated, you can perhaps skip this, but it doesn't cost much, is easy to do (especially easier now than later), and will doubtless help some either way.
For this type of job just pick up some rolled insulation that was made for 16" walls. There will be paper flanges that you can staple to the studs. Measure out a length and cut the insulation with a framing square as a guide, and a utility knife. Use a scrap piece of plywood as a cutting board (I wouldn't use your hardwood floor or even carpet, you won't be happy with the results and will have to buy a large rug).
I typically cut the piece about 4 inches longer than the measurement so that I can pull the insulation away from the paper about two inches at each end. Don't remove the insulation, just pull it away and roll it up at the ends so that you can use the vapor barrier to overlap the framing. Go all the way around the shaft.
Hanging The Drywall
I would recommend you hange one of the side pieces first, this is because, with the angle and all, you might be off a bit and you can hide it easier if you end up with a normal, straight piece. Let's say you you are standing at the 'tall' end of the skylight shaft. You are facing the 'short' end. You're going to start with the angled piece to your right. So measure from the bottom corner to the top corner on the
long side. Then measure from the bottom corner to the top corner on the
shortside. Now measure the distance across the bottom edge of where that piece will go, that will be from the bottom corner on the long side, to the bottom corner on the short side.
