The calculations for a stairwell, especially the rise and run and the carriage (stringer) layout and dropping, are critical — I recommend the classical treatise on the subject, Basic Stairbuilding by Scott Schuttner.
The corner walls where the staircase was to be fitted were paneled by a tongue-and-groove wainscoting (diagonally-nailed tongues), with cutouts for electrical appliances and the hangerboard. We used a simple design of ‘cut carriages’ (which yields an open-rise stair), rather than the more labor-intensive alternative of a housed stringer (aka closed skirt). The three carriages were laid out by the framing-square, sawed with a circular saw and finished with a handsaw. The bottom of the carriages is notched and anchored to the kickboard, which is nailed to the subfloor. A single step originally present in the subfloor was filled with a heavy-duty decorative wooden fillerboard. The fillerboard was fashioned from multiple wood types and pieces of different thicknesses and textures to create a characteristic surface pattern. After hanging the carriages on the hangerboard we installed the treads and risers (the treads were ripped on a table saw, crosscut to length and rounded over the nosing with a router) with a construction adhesive and screws. Finally, the staircase was trimmed by adding a mitered skirtboard with spacers in-between. The treads have mitered returns (moldings) to hide the end grain. Small shims were used where needed to take up gaps between the treads and risers and the carriages.
