A sharp axe is a safe axe. Dull axes not only make your work harder they can glance off the wood and cause serious injury.
Tools needed to sharpen an axe are a file, a honing stone, and a strop. A flat, mill bastard file should be used if your axe is extremely dull or chipped. After using the file (if needed) finish with a flat or puck style medium and then fine hone. Use a leather strop to complete sharpening your axe.
When sharpening your axe be mindful of the bevel or angle at the bit end. An axe is not a straight consistent wedge. The angle of thickness is different as you move up the axe bit. Most axes have a 30-40 degree angle at the end of the bit and a 15-20 degree angle about ½” from the cutting edge. The bulge away from the end of the bit is what provides the axe its splitting power.
Never sharpen your axe on a bench grinder as the heat generated by the wheel can cause the axe to lose its temper.
There are many excellent videos on line to teach this skill:
See also: Sharpening, Thomas Lies-Nielson, Taunton Press: Newtown, CT (2004)