Hang the Sheetrock on the wall and over the door opening and secure it to the studs with the drill and drywall screws. The first piece of Sheetrock should be hung on the wall so it meets the ceiling. The Sheetrock also needs to be fastened into the studs framing the door.
Place the hand saw along one side of the door jamb with the blade pointing up, and then cut the drywall from the bottom up, until you reach the top of the doorway. Do the same along the other side of the door opening.
Stand on the side of the doorway so you are looking at the back side of the Sheetrock. Use the utility knife to score the Sheetrock along the top of the door opening, and push on the piece to snap it.
Face the front side of the Sheetrock and use the utility knife to cut along the snapped line and completely remove the scrap piece of drywall.
Install the next piece of Sheetrock so the top edge of the Sheetrock is butted up against the bottom edge of the first piece.
Cut the Sheetrock along both sides of the jamb, this time with the hand saw on top of the Sheetrock with the blade facing down. Remove the scrap piece of Sheetrock.
Install a third piece of Sheetrock, if necessary, depending on the wall height. Once it's screwed in, cut along the door jamb with the hand saw.