Set the chair on a workbench to remove the old caning material and spline. Loosen the existing spline by running a utility knife or a thin-bladed chisel along each side of the spline. This will break the spline away from the frame.
Push your spline chisel into the spline starting at the front of the chair. Pry up the old spline. If it's stubborn and does not come out in one piece, pry it out in pieces until you get to the bottom of the groove.
Turn the chisel on its edge and continue to scrape out the groove until the old spline is completely removed. Roll up a piece of fine grit sand paper and run it through the groove to remove as much glue residue as possible. Remove the old cane material.
Measure the length of the groove and cut the new spline 2 inches longer. If the groove has tight rounded corners, soak the spline in a bucket of warm water to make it more pliable. If the groove has square corners, measure four pieces to length with a 45-degree miter cut at the ends. Use a utility knife to obtain a clean angled cut. Take note as to which groove the pieces fit into. These do not need to be soaked; simply set them off to the side.
Measure and cut the new cane material allowing an extra inch on all sides. Dampen the material using a wet sponge. With the shiny side facing up, position the cane making sure that it evenly overhangs the grooves.
Hold the cane in place and hammer a wedge into the middle of each side. This holds the material in place while you push it into the groove. Using your mallet and a thin wedge with rounded corners, start at one side and work your way around the entire seat pushing the cane material into the groove.
Trim away the excess material using your utility knife or chisel. The material should be trimmed so that it is halfway up the outer edge of the groove.
Put a bead of glue into the groove around the entire seat. If you have four cut pieces of spline, simply hammer each piece into the correct groove with your mallet. Otherwise, remove the spline from the water and dry it off. Make a 45-degree miter cut at one end.
Begin at the back of the seat and hammer the mitered end into the groove. Work your way around the seat, hammering in the spline as you go. When you get to the end, line up the spline with the first angled cut and make a corresponding angled cut. Hammer the end into the groove.
Finish the project by wiping away any glue that has oozed out of the groove during the installation.