Attach the axe blade to a work bench using a C-clamp. Begin filing into the dull edge of the axe with a mill bastard file. Work toward the center of the axe handle to create fewer burrs on the opposite side of the axe. Move towards the "cheek," or flat portion of the axe that leads up to the head, using fan-like strokes. File as far back as 2 inches to 3 inches from the edge. When you feel the burr on the opposite side, turn the axe and repeat the steps on the opposite side.
Remove the burr from the axe edge with a wire brush. Test the shape of the axe edge using a sharpening gauge. The gauge can be handmade. Simply cut a V-shape into cardboard. Check to see that the angle of the blade is 25 degrees. If the V-shape does not fit over the edge, continue filing for a perfect fit.
Polish the sharpened axe edge using a sharpening stone. Apply finishing oil with a cloth to add a renewed shine and to protect it during use.
Maintain the edge on your axe with proper care after sharpening. Never leave the axe outside where it is exposed to harsh elements. Prevent rust and dulling by keeping your axe head in a leather case when it is not in use.