The process step by step Edit
Take a piece of wood that has some natural curvature; the curvature prevents the grain from being cut through too badly:
Roughly form the back of the piece with an axe:
Do the same for the belly:
Plane the sides straight in a vise:
Plane the back flat and perpendicular to the sides:
Attach the piece belly-side up to a vise:
Carve, plane or rasp the belly to correct curvature. Chisel the hole for a rectangular, wooden rivet into the middle of the crescent-shaped piece.