They both must be very dry but not rotten. The handle can be of any material. There should be a shallow hole in the handle to fit the drill. It does not need friction. The tinder must be of very fine materials.
Traditional materials vary from region to region.
Flatten the bottom piece of dry willow or alder on two sides. Twist the drill into the string of the bow. The drill should be on the outside of the string, not the inside. If it is on the inside, it will jam between the bow and the string. Put a large quantity of tinder under the bottom piece of wood.