Timothy, do you know what kind of cane or reed you have there. Do a little research and find out. Your local farm agent or Cooperative Extension Service can help you with that. Then research what shafting the local Native Americans used and the method they used to build arrows.
Our "How To" section has lots of info about building arrows from local materials. Patrick(Jackcrafty) has a few excellent How To's on Native arrows with excellent instructions and explanations.