Measure the distance from the midpoint of the wall stud nearest to the bottom of the stairs to the beginning of the first, or bottom, stair step. Subtract 3/8 inch from that distance, record the measurement and draw it on a chart. Measure the height from the floor to the top of first stair step, and add that measurement to the chart. Measure to the bottom of the next stair step, subtract 3/8 inch and add the measurement to the chart.
Continue that procedure until you've sketched the step dimensions onto your chart. Always subtract 3/8 inch from the horizontal measurement to allow for fitting tolerances. The vertical 3/8-inch tolerance will be added when you install the drywall sheets. The slight gaps will be covered by baseboard trim installed after the drywall is up.
Transfer the measurements to your first sheet of drywall. Put on a dust mask, and cut the drywall sheet with a jigsaw to match the measurements. Use a drywall blade on the jigsaw.
Place 3/8-inch thick shims on the floor and stair steps. Place the cut drywall sheet on the shims, and slide the sheet until it is positioned properly above the floor and steps. Screw the drywall to the wall studs with drywall screws, placing the screws every 16 inches up the studs. Pull the shims from underneath the drywall sheet.
Cut your next sheet of drywall to match the dimensions you've recorded for the next set of steps, starting at the end point of the first drywall sheet. Install the second drywall sheet in the same manner you placed the first drywall sheet, including using the shims. Cut and install subsequent drywall sheets in the same way until the staircase wall is covered with drywall sheets.
Place joint tape smoothly on the seams between the drywall sheets. Spread joint compound over the joint tape using a drywall knife, and feather the edges of the joint compound with the drywall knife, lessening its appearance gradually on the drywall. Let the joint compound dry. While wearing the dust mask, sand the dried joint compound until it is smooth. Afterward, the drywall is ready for primer and paint.