Use full sheets of drywall whenever possible. Cut the length of the sheet so that the end falls in the center of a joist or stud.
To cut a sheet for length, first set it upright with the finish side out. Measure out the length with a tape measure. Then using a drywall T-square on that mark as a guide, score the front side with a utility knife.
Snap the drywall back. It should break apart right at the cut. That doesn't cut the paper on back, though, so to finish the cut run the knife blade down the back side to cut the waste free.
Making cuts along the length of a sheet is a little trickier. One way is to snap a chalkline along the sheet and then score the line by hand. Be aware, though, that sometimes the chalk will bleed through the paint. If you have an 8' straight edge that would work, too.
Another way to make this kind of cut is with a tape measure. Hold the tape measure in your left hand with your thumb and fore finger at the dimension you want. Hold the blade of your utility knife under the end of the tape, holding it against the hook. Now run your left hand across the top of the board, and score the drywall with the knife. This is not a super-accurate method, but it's good enough for hanging drywall.
When you need to cut inside corners, cut one side with a drywall saw. Then score the other side with a utility knife and snap it back like you would any other cut.
Another way to cut inside corners is to first install the piece, then cut it with a drywall saw along the framing.
Cutting for Lights, Switches and Outlets
Cutting holes in drywall for lights, switches and outlets requires careful measuring and marking.
For round light fixtures, like recessed lights, measure from the edge of where the drywall sheet will go to the center of the circle. Do this from both the side and top. Then transfer these measurements to the sheet of drywall.
Use this mark for the center of your circle hole cutter. Also measure the radius of the round fixture to set the arm length of the cutter. Score the circle several times, then tap it out with a hammer.
You can also use a compass to draw the circle and a keyhole saw to make the cut.
For switch and outlet boxes, measure from the side edge of where the sheet will go to the right and left side of the box. And measure from the top edge to the top and bottom of the box. Transfer these to the sheet of drywall and cut it with a keyhole saw.