My African folding chair cracked lengthwise.
I fixed it with epoxy thickened with wood dust. That's usually the best thing, but use whatever you've got. Even Elmer's school glue is okay if the crack isn't separated too far.
If you're fixing a valuable musical instrument talk to a luthier about glues. They'll suck you into a glue-filled time-vortex.
Step 1: Clean the Injury
I pried the crack apart and sanded as high in the crack as I could. Then I pushed the crack together to sand the outer part.