Apparently one method archers use is to cut a long, angled splice with a new piece, as seen in the image below. The angle is meant to provide a large surface area for glue.
However, this "conventional method of repair can sometimes not withstand the shear force caused upon impact, thus resulting in breakage upon the repaired area," according to the makers of Arrow-Fix, a specialty German tool that takes a different approach.
The Arrow-Fix tool contains both a sharpening mechanism and a special drill bit:
It can be attached to a power drill or used by hand. It's used to cut both positive and negative conical tapers:
These then fit together, using a minimal amount of glue:
If you feel like you've seen this before, it is awfully similar to the Tsunago, a Japanese invention we covered here, that does the same trick with pencils.