You can start sharpening nicked or seriously dull axes with a bastard file (no, I don't know why they call it that). You don't want to sharpen "into" the blade (from sharp edge toward the handle), as this causes you to risk pushing the file too far and cutting yourself. File from the back of the axe head, toward the edge and out. This does create more of a bur than filing the other way, but it's faster to remove a bur than regrow a fingertip. Work both sides of the axe equally, counting strokes if you want to get it perfect. File until the blade edge is beginning to feel sharp again, and any chips or nicks in the edge have been eliminated.