Hold a piece of chair rail on the stairway wall so that it is parallel with the slope of the stairs. Hold a second piece of chair rail along the horizontal installation point on the wall at the bottom of the stairs.
Overlap at least 3 inches of the stairway chair rail with the chair rail at the bottom of the stairs so there is enough edge to mark the angle.
Make a pencil mark where the top and bottom points of each section of chair rail meet. Connect the marks with a ruler to create a straight line on each section of chair rail.
Cut the stairway chair rail along the pencil line with a miter saw for a clean cut. Fit the slanted ends together on the wall to verify that the angle is correct for the chair rail's desired placement. Make adjustments to the angle if necessary.
Sand the cut edge of each chair rail section lightly to smooth out the wood. Install the chair rail onto the wall.
Repeat this process with the chair rail at the top of the stairs and any joints needed along the stairway.