Cuts to length are always made with a knife and drywall square.
Door cuts are done by sawing up _or_ across, and cutting from behind the other leg of the ell. Lite/box/duct cutouts are usually marked for center and cut after hanging - with a router. I make narrow rips for doorway edges on the table saw, that's the cleanest cut of all.
For cutting lite boxes, etc, a down-cutting jigsaw blade would be perfect. The teeth are reversed, and cut on the downstroke.
Casey

The cleanest cut paper wise will be to cut the outside with a utility knife, break at the cut, and cut the back side. This method will leave a ragged edge on the drywall itself, but a smooth line on the paper.

The cleanest cut edgewise is to install the piece and use a rotary tool with a sheetrock bit following the contour of the box/window/door outline.This method will leave a smooth edge on the drywall, but a feathered edge on the paper.

Cutting with a drywall saw can leave ragged edges on both paper and drywall.

The only way to leave a finished looking edge is to score the drywall from the back, break the drywall material away from the front paper, and fold the front paper around the edge, gluing or taping the end of the paper to the backside of the sheet.

You're correct to cut the finished side with a drywall knife.
With practice, and there is a short learning curve, you can make all of the cuts with a tape measure and a drywall knife.
The exception being opposing cuts in the same sheet. There both legs are scored with the knife and one is cut with a keyhole saw or a drywall saw.

The use of motorized saws and cutting tools create a lot of unnecessary dust for a small project.

Thanks all. I do have a bit of a learning curve here. I had some skylights put onto my roof during a recent roofing job. They only did the outside part and left me with the inside. I ran out of money to hire someone, so I'm doing it myself. Luckily in the case of the corners of the shaft, there will be overlap, so pretty is not a priority. I'm just a little lost as to how to make it all meet up nice and clean when it gets to where the ceiling is. I didn't think about attaching the piece first and cutting later. Maybe that's the way to go. I have a router, but can't really say I'm aces at using it. Do you just cut "freehand" or attach a piece of wood at a guide? So far I've only used it with projects involving templates. I've got extra material, so I'll try a few practice cuts.

By the way, how do you attach the shaft pieces to the ceiling pieces where they meet at the 90 degree angle? Is that just tape and compound?

Hi,
The light well/ceiling corners would be done with corner bead, "available wherever drywall is sold".
At the edge abutting the skylight, there may well be a 1/2" wide rabbet in the skylight's edge (Velux has this) to accept drywall or 1/2" plywood. This will call for some precise measuring/fitting to get it right. A roto-zip router is usually riding its bit end on whatever thing you are cutting around, be it framing, an electrical box, etc.
Casey

Yeah, these skylights do have that edge to fit the drywall. That part I have figured out. It's just getting the clean finished edges I'm concerned about. I'll look for that corner bead stuff to see how that works.

Then, there is crown molding, casing and indirect lighting.

I like to mark my line in pencil first. Then, place a drywall cutting T-square on the piece with my free hand and knee holding the T-square firmly down. Carefully cut along the edge of the T-square with a sharp utility knife - it doesn't have to be a real deep cut. Place the square so that if your knife strays off the mark, it will not cut into the piece you are using.

After the cut is made, carefully lift up the sheet and stand on edge. Hold both edges of the sheet and push at the back side of where you made your cut with your knee - the drywall will break cleanly along the cut. Fold the two halves about 45-90 degrees and then cut at the fold of the back side with a sharp utility knife taking care so the pieces do not rip apart before they are completly cut - it may be helpful to support one half against a wall (or have a helper hold the pieces) and hold onto the other half as you cut.

For more info and a pic of the T-square I am talking about, check out the link below.

Here is a link that might be useful: How To Cut Drywall