Duke William of Normandy won the battle because was well prepared and had a good army. They prepared carefully for the battle. The Normans had knights on horseback who were skilful fighters.
A utility knife, metal ruler, and a hammer can be faster than trying to carefully saw an opening. Score the drywall a couple times till you are most of the way through, then just knock a hole with the hammer and break the drywall back at the score lines.
What I've done before is position the drywall and had a helper push up gently against the fixture (light can, electric box, etc.) and then bring it back down. This makes a mark on the back so you know exactly where to cut. A rotozip works great but I prefer to use a hole saw for round holes. Six6's method would not break the sheetrock, it has enough give to bow over the fixture while you cut out the hole. And you could use a hand saw and utility knife instead of the rotozip - it won't be as pretty, but that's what the trim ring is for...