Measure the ceiling so that you know exactly how much drywall you will need. Drywall comes in 4 by 8 foot sections. The object is to use as many full pieces as possible. Start at one corner and work to the opposite diagonal corner. Determine where your cuts will be made.
Hang all the drywall on the ceiling that is full sheets. You will have to adjust the scaffold as you go since the vaulted ceiling will angle upward. Put the drywall in with the drill using drywall screws. Make sure the screws are 12 inches apart and that they go into the ceiling joists.
Measure and cut all of the pieces that are needed to finish the ceiling. Hang them in the same manner as the large sheets.
Fill all of the screw caps with drywall mud using the putty knife making sure the mud is flush. You want to have about 1/16 of an inch on the screw caps. Tape all of the gaps between the drywall and then mud over them using the putty knife. Again make sure that the mud is about 1/16 of an inch. Make sure it is smooth. Allow to dry for two hours.
Sand all of the screw heads and the tape spots until they are smooth. Again this will cause you to adjust the scaffold. Apply the mud to the screw heads and gaps the same as in step 4 once more and allow to dry for two hours. After it dries sand until smooth.