You have to be in a place where you can jump off of a cliff and have enough time to swing your deku stick at an adjacent wall. The best place is in the kokiri forest near the entrance to the lost woods. Before you jump, pull out your deku stick. Once you jump, press the deku stick button to hit the wall. It will count as the stick breaking, but you will still be holding half of the stick. It is stronger than your sword, but if you leave the area it will disappear.