Measure and mark five equal lengths from one side of the back of the stool seat to the other. These marks should be inset 1 to 1 1/2 inches from the back of the seat.
Choose a drill bit that is the same width as the bottom peg on the pre-fabricated spindles. Drill a hole the same depth as the peg at every spot you marked on the stool.
Fill each hole with wood glue and insert the pegs of the spindles.
Measure the length of the back of the stool. Cut this length from the 2-inch-by-8-inch board with a circular saw to use as the upper back brace.
Sand the top and sides of the upper back brace with an electric sander.
Measure and mark five equal sections on the bottom of the upper back brace. Drill them in the same way as you did the spindle holes on the stool.
Cover the top of the spindle pegs with wood glue and slip the back brace into place. Wipe away any excess glue with a piece of scrap cloth. Allow the chair to dry overnight.
Stain the new back brace and spindles to match the stool.