Step 1: Cut the stairs to match the width of the original stairs.
|Staircase cut down to correct width|
In the picture above you can also see that I added a piece at the bottom to create more of a base for the stairs.
Step 2: Adding the base. I just cut 2 triangular pieces of balsa wood and glued them to the bottom.
|Triangular pieces added|
|Staircase base detail|