Free Hand Utility Knife Technique
I personally have good luck with a utility knife freehanded. I use a straight edge to mark a straight line, often with a pencil instead of a utility knife. If you do use a utility knife with the straight edge, ensure you are keeping the knife vertical and don't apply too much pressure. Too often the blade will carve out the drywall under the straight edge, or pressure against it will push the straight edge off of it's mark.
The trick to straight freehanded lines is to use your body rather that your wrist. If you try to correct your line by shifting your wrist, the line will be all over the place. If instead you push the knife with your shoulder and elbow, keeping your wrist locked in one position, your lines will be much straighter.
Drywall Bit on a Rotary Tool
Probably the easiest method to cut drywall is with a rotary tool. Have someone hold a straight edge, or practice cutting straight lines freehanded since this tool will tend to push to the side. The advantages of these tools are speed, ease of use, and they can be adjusted to not go too deep so you don't run the risk of hitting utility lines behind the drywall.
This is not a recommendation for a specific vendor, sample images only.