Installing a skirt board on a staircase requires some time and preparation to do properly. You want top make sure your cuts are square, and that the skirt board fits properly and without gaps.
Install the risers of the stairs, making sure that the risers are plumb when you do so.
Place the skirt board over the riser's top, making sure you follow the rake of the staircase. Tack the skirt board in place so it won't move as you install a staircase skirt board.
Set a level against the riser's face, and run a pencil along the level, marking the riser's front and the skirt board as well.
Use a framing square to make a line that's 90 degrees from the riser's top. Repeat the process with all of the risers as you install a skirt board on a staircase.
Remove the skirt board, and cut along all of the pencil lines you have made to create the rise and run.
Slip your skirt board into place and check the fit. Make any adjustments as needed as you install a skirt board on a staircase.
Secure the skirt board in place, then cut the treads of the stairs so that they will fit in between the skirt boards. You may wish to allow a few extra inches on the treads as you cut them, to counter any shrinkage that might occur.