Begin with a chair that has all the old cane removed and, if you wish, has been refinished. Use pieces of the old cane to purchase the same weight of new cane. Soak the new cane in warm water and two tablespoons of glycerin for 20 minutes before you begin. Roll the damp strands of cane loosely and set aside.
Locate the center holes in the chair frame front and back. Thread the first length of cane through from the back center hole to the front. Use a small dowel or pin to hold the first end in place, then continue threading the cane through the front hole, up through the next, then back to the back holes. There should be some give to the cane, and be sure it does not twist. Use pegs to hold the ends of the strips in place.
Thread the cane in the same manner horizontally across the chair, running the canes over the top of the vertical strips.
Thread a second set of vertical canes over the top of the first set. Begin, as before, at the back center hole. Turn the chair over and tie off any loose ends beneath the chair when you are done.
Weave cane horizontally, beginning in the upper right corner hole. Weave the canes over the top vertical cane and under the lower vertical cane.
Weave diagonally across the chair seat from the upper right corner hole to the lower left. Go over the vertical cane and under the horizontal. Weave toward the back left half of the chair seat, then do the front half.
Weave diagonally in the opposite direction, from the upper left corner to the lower right. Go under the vertical cane and over the horizontal. Weave the back half of the seat first, then the front.
Finish by weaving in the border cane, which is wider than the seat canes and is used to cover the holes and create a finished look. Insert the end of the border cane in the back corner hole, then loop regular cane over the top of it beginning at the next hole. Run the cane over the border cane, then down the same hole and up through the next, continuing around. Continue until all sides are finished, then tap a small peg or dowel into the final hole with a bit of glue to hold the border end in place. Tie off and trim any loose ends beneath the chair.