with really bad axes i do the following, even though in every peice of written info out there, it is strongly advised against:
i start with a coarse stone on the bench grinder. this is solely for getting rid of the metal. i keep my fingers right behind the edge, and dunk and swish in cool water very frequently. i to this for thinning the edge down, since most axes are far thicker than i want them to be.
after the heavy grinding (depending on what kind of finish i am going for) i will take it to a coarse belt on my 1x30 belt sander, around a 40 or 60 grit. i smooth out and flatten up the heavy grinding marks, and make sure everything is still straight.
i then set up a convex edge bevel, sometimes one smooth bevel about 1" wide or more, something like a full convex. sometimes a flatter edge with a small, knife-sized convex bevel. depends on my mood.
my first couple of axes were modern collins, and i found that they cut with a good file pretty well. i suggest a large (the larger the better...i have a 14" sitting in reserve) single cut bastard file for the heavy removal. attach a handle and some sort of guard (sheet of brass, aluminum, wood, leather, etc) to help reduce the chance for injury when filing towards the edge. also always wear heavy gloves for the same reason. once the edge is really nice and even, and you have a burr along the whole thing, then take it to the stone to polish it up. then i took them to some coarse grit sandpaper backed with a mousepad, and polished it up to about 1200 grit for a crazy sharp edge.
check out this site:
http://blueandwhitecrew.org/resources/tips/sharpeningaxes.php
it's a little bit more in-depth than i usually go, but its alot of good info.
