Fiskars 7861 Axe and Knife Sharpener
Buy new: $8.99
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If one really wants to put a razor sharp edge on an axe or knife, a set of diamond whetstones is the best way to do it. This painstaking manual process requires time and proper technique. Beware: a razor sharp edge is exactly that and not to be trifled with. On the other hand, if "pretty darn sharp" is good enough...and it should be for most utility purposes...a dedicated sharpening tool like the Fiskars will get the job done quickly and with minimum risk to one's fingers.
Fiskars 7861 Axe and Knife Sharpener