Measure the rise and step of each stair. The rise is typically 7 inches and the step 10 inches, but each may vary on individual stairs.
Recreate the rise and steps of the stairs on the bottom of a full sheet of drywall. Begin at the bottom edge and measure upward the distance of the rise. Use a measuring tape and level to draw a line over the width of the step. For example, measure 7 inches up the edge of the drywall, then over 10 inches if the steps are traditional size. From the end of the step marking, repeat the rise measurement then the step measurement. Repeat to the edge of the drywall sheet or for the number of steps in the stairs. If necessary, begin the process again from the bottom of a second sheet of drywall.
Cut out the recreated stairway on the drywall. Use a knife to carefully follow the drawn markings.
Attach the drywall over the stairs. Place the first piece flush to the stairs, beginning at the landing and moving upward. The bottom of each sheet will sit against the steps.
Measure the area under the stairs and cut 2-by-4-inch boards to the staircase's length. Attach the cut 2-by-4s to the floor, aligning the outer edge of the boards with the outer edge of the stairs. Use a drill and concrete screws for a concrete floor or a hammer and nails for a wood floor.
Cut 2-by-4-inch boards to the length of the underside of the steps. Cut one board for every 4 steps. Attach the boards, wide side under the step, with 3-inch nails. Attach one to the top step and one every four steps.
Measure from the floor to the bottom of the highest step. Mark this distance from the bottom of a full sheet of drywall. Measure the width of the step and then the drop of the rise. Repeat this pattern and distance on the sheet of drywall. Repeat the process, measuring over and down to the edge of the drywall sheet or until the number of stairs is reached. If needed, measure the stopping point on the stairs and begin again on a second sheet of drywall.
Cut the drywall with a knife along the drawn lines.
Attach the drywall to the 2-by-4-inch boards at the top and the bottom. Align the cut drywall with the stairs and use 3-inch nails to hold them in place.