Use a caning chisel to carefully chip away the old glue. Be very careful if you're using a sharp knife or you'll risk damaging the chair itself.
Never place your hand in the path of the chisel!
If the glue is not responding to the tool, wet the glue in the groove with some vinegar and let sit for a while. The vinegar should soften the glue and make it easier to proceed.
If the glue doesn't respond to vinegar, make your life easier and use De Glue Goo®. This product is amazing. De-Glue Goo® is the only non-toxic gel that will dissolve hide glue, white and yellow glues quickly and easily. We guarantee that De-Glue Goo® will dramatically cut your spline groove cleaning time. If you've got hard glue in the groove, don't forget to order this. It's amazing stuff, for sure. You won't risk hacking away at the chair groove if you get this product. We highly recommend it.
When installing the new cane webbing, use any brand of white glue for indoor chairs. Do NOT use carpenter's glue or other heavy duty glues.
For canoe seats, be sure to use a water proof glue, not a water resistant glue.