Remove the stair tread with a 7-inch pry bar. Insert the flat front portion of the pry bar between the tread and the riser at one of the ends of the tread. Pull up on the pry bar to loosen the tread. Move the pry bar along the front of the stair tread, gently lifting the pry bar and loosening the tread as you go.
Remove the loosened tread from the stringer.
Apply construction adhesive along the top of the stair stringer.
Set the new stair tread on top of the stringer. Press on the tread to form a bond between the stringer, the adhesive and the tread.
Hammer finishing nails along the top edges of the tread, driving them through the tread and into the stringer. Place finishing nails every four to six inches along the edges of the tread.
Place a nail set over the heads of each of the finishing nails. Bang a hammer on top of the nail set, driving the finishing nails into the tread.
Fill the holes in the stair tread above the finishing nails with putty that matches the wood of the tread.
Sand the tread with fine-grit sandpaper. Vacuum the tread and wipe it down with a tack cloth to remove sawdust. Stain the staircase with polyurethane stain.