Sketch the area that you want to put drywall into. Measure any straight lines in the area under the steps and put the measurements on your sketch. Measure the distance between each corner and mark these measurements on the sketch.
Determine the location of curved corners. Choose a corner that is a right angle (90 degree angle.) Find the distance from that corner to two other right angle corners. Make a line on your sketch from each of the two corners to the corner that is not a right angle corner and make a curve at the end of the line. The intersection of the two curves is the location of the non-standard corner.
Redo your sketch on a sheet of one-quarter inch drywall. Choose a corner of the sheet to use as a right angle. Use a level with measurement markings as a compass to help you draw curves.
Install the drywall. Match the sketch up with the actual staircase. Put starting screws into the drywall where it meets wood joists. Use a screwdriver to put screws in along the lines of the sketch. The drywall will bend to conform to your sketch. Insert the screws all at the same angle to avoid ripping the drywall.
Check the drywall after a day for signs of ripping or tearing. Remove any screws that are inserted at the wrong angle and re-insert them. Insert more screws if the drywall seems loose.