It cannot be stated strongly enough how important it is for your cutting tools to be sharp. Sharp tools are far safer than dull ones and will do more work with less effort. You need to learn how to sharpen every cutting tool you own or use.
Sharpening An Axe
Abraham Lincoln is reported to have said: “Give me six hours to chop down a tree and I will spend the first four sharpening the axe.” The tool of choice for an Axe is “The Puck” which is a round sharpening stone with a course and medium side. It works fairly well but does not produce a fine edge because it does not have a fine grit.
If an axe or hatchet is really bad you will need a file or grinder to re-profile the cutting edge. A file might be the safest for someone new to sharpening, as it is much harder to mess up the edge by hand.
Be careful using any power grinder when sharpening that you do not heat up the metal and draw out the heat treat. One tip is to hold it barehanded as you can feel it if the heat starts to build up. Some kind of belt sander/grinder is what you want if you want a shiny finish. You can sand by hand, but that takes a fair bit of time.
Page 27 of “An Axe to Grind” have more information about sharpening and page 29 has an Axe-Bit Gauge you can print.