Clean and polish the head
You can use steel wool or a rust eraser to remove all the rust if any then sand the entire axe head with rough-grit aluminium oxide or silicon carbide sandpaper. Then go over it with a finer sandpaper and a third time with even finer sandpaper. Next polish it with polishing paste applied to a felt pad or rag getting the whole head with an even coat.
File the blade
Either clamp the axe on to a worktable on its side or into a vice. Then get a bastard file with a finger guard to file the blade with some form of protective glove recommended. File toward the blade only, do not make contact on the return stroke, and use a file card or brush to remove metal build-up on the file. Continue filing evenly along one side until a burr of metal appears on the other side. Then swap sides and repeat.
Hone the blade
You should do this every time you are going to use your axe. Apply honing oil to the blade using an oil stone then water using a water stone. This helps remove the metal particles. Then work into the edge of the blade using the rough side of a two side whetstone in a circular motion. Do this until a burr appears then switch sides and repeat. After this process do the exact same thing with the fine side of the whetstone.
When finished rub a beeswax and oil mix into the steel when warm to protect against future rust.