How do I cut drywall on the ceiling accurately?
Utility Knife

Position a 2'- 4' level (or other straight edge) along the line you'd like to cut.
With the straight edge in place, gently draw the utility knife along the line. You don't have to press too hard, just enough to cut through the paper on the face of the drywall.
Draw the utility knife repeatedly through the groove you scored in the previous step.
Increase the pressure slightly with each pass.
Continue until the knife has cut through the drywall.

Once you score a line in the drywall, the utility knife will tend to follow the groove. So you'll only need to hold the straight edge in place for the first scoring pass.
Drywall Saw
You should be able to pick up a drywall saw at any hardware or home improvement store, for just a couple bucks.  These saws have a sharp pointy tip, which makes plunging through the drywall easy.  They also have coarse teeth, which make cutting the drywall easy.

They are often known as &quot;jab saws&quot;, because you use them by jabbing them through the drywall to start your cut.

Place the tip of the blade where you want to begin your cut.
Smack the hilt of the saw hard, to force the tip through the drywall.
Carefully make your cut using a back and forth sawing motion.

Power Tools
You could also use a rotary saw, or oscillating Multi-tool to quickly and easily cut drywall.


WARNING:
Always be aware of what is behind the drywall, to avoid cutting into wiring, plumbing, or other hidden dangers.