Measure the length of the staircase and record the number of steps. Log onto an online source for wainscoting and use the design tool to purchase the recommended pieces to complete your project.
Paint the walls of the staircase ahead of time if you're planning on it -- this will be easier than painting the walls after the wainscoting has been installed.
Use a stud finder to locate and mark the studs in the walls of the staircase. When you nail the wainscoting panels to the stair wall, you'll get much better purchase with the nails if they hit a stud.
Place the panels in position to check their fit. Start at one end of the staircase and spread construction adhesive onto the back of the panels then place them on the wall of the staircase. Nail the wainscoting panels to the studs with 6d finishing nails.
Prime and paint the panels after they're installed.