Set up the scaffolding in your stairwell prior to hanging the drywall. Have your helper work with you to hold the opposite end of the scaffolding while you lift the bracers into place that make up the sides. One set of legs will be higher than the other due to the stairs, but once the ends and braces are set, you can set your platform level across the two ends to create a safe and flat working environment.
Measure the area for your drywall. Check if you can install a full sheet in the work area. Plan any cuts so that the drywall will split the joists and the adjacent piece will have somewhere for the screws to mount the board in place. Make your cuts on the ground.
Place the drywall in a vertical position, leaned up against a wall. Mark the piece according to the size of your cut, and cut it. Place the T-square along your mark and cut the face with a utility knife, using the T-square as a guide. Bend the piece backward across that scored mark, and cut the back side with your utility knife to complete the cut.
Work together with your helper to lift up the piece of drywall and hold it in place. You'll install it so that the edge of a piece only rests halfway across a ceiling joist to provide space for the next adjacent piece.
Sink screws into the corners as well as the middles of the pieces along the perimeter to mount the piece, and then sink screws every 3 or 4 inches across the entirety of the sheet along the ceiling joints. Repeat the process for all of your pieces and finish the ceiling as you choose, such as with drywall mud, wallpaper, tile or plaster.