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Begin by removing the existing stair components. Use a circular saw to make relief cuts on the old treads and risers. Follow up with an oscillating multi-tool to cut into tighter corners and edges where the circular saw cannot reach. Then, use a prying tool, such as a pry bar, to carefully loosen and remove the old wood pieces from the stair frame. Once the bulk of the material is removed, use an angle grinder fitted with a sanding disc to clean up any remaining adhesive, paint, or uneven spots on the stair subfloor. Finish by thoroughly vacuuming the area with a shop vacuum to remove all dust and debris, creating a clean surface for the new installation.