Wet the old cane and cut with a utility knife. Remove as much as possible. Dig the blade vertically into the groove where the spline is embedded to break the seal. Use a screwdriver or spline chisel to pry up the old spline. Remove any nail or staples with needle nose pliers.
Clean the groove completely, removing old glue. Use the edge of a screwdriver or a spline chisel. Use a small amount of vinegar to remove any stubborn glue.
Check for rough spots and sandpaper these areas with a fine-grit sandpaper.
Refinish the chair, if you are planning to do so, while the cane is off. If more than one area of cane is on the chair, plan to replace all of it at one time.
Measure the area to be covered by cane and add four inches. Measure the circumference of the groove and add four inches for the spline. Cut the sheet cane with a utility knife or scissors. Cut a single piece of spline to measure.
Soak the cane and spline in a warm water bath for at least one hour. Remove the cane but leave the spline in the water until you need it.
Position the new cane over the chair, centering it and making sure it is straight and the shiny side is up. Secure it into place with clamps at the bottom corners with clamps or small pieces of spline.
Begin pushing the cane into the groove, starting at the back center and using a wood wedge. Wet the cane every few minutes with either a damp sponge or rag or a mist sprayer.
Work the cane into the groove a bit at a time, going back and forth from one side to the other until you get to the front. Don't force it all the way into the groove, just enough to hold it into place. Use small pieces of spline to anchor your work in place. Check your work often to make sure the cane is straight. Remove the clamps when you get to the front and keep working the cane into the grooves until you complete this step.
Insert the new spline by first putting a bead of glue into the groove all the way around. Place one end at the back center and pound the spline into the groove with a rubber mallet or hammer. If the cane has a corner, miter the spline with your utility knife. Cut off excess spline at the back center where the two ends of the spline meet.
Wipe off any excess glue. Cut off excess cane carefully with either the utility knife or scissors.
Moisten the cane again. Place a damp cloth over it and leave it to sit overnight. Carefully cut away any stray pieces of spline or cane with scissors. Wait 48 hours before you use the chair.