Wipe it dry, keep away from the damp and that's about all there is to it. If the shed is damp then some WD40 like Navek said. Don't leave it propped up where you could walk into it unless the edge is covered. An axe mask can be made from some ply or leather.
If left in a damp area, some people favour leaving the axe stuck in a log so that the cutting surface isn't exposed.