I'm not a sharpening expert by any means (at all), but what I've gathered from YouTube led me to use a file to get the overall profile, and some time with a Lansky sharpening puck to get things pretty sharp.
I'd abused the **** out of my ax - I bought it at Sears in the late '90's and had used it to break up stuff in my yard when I was installing beds. The "stuff" turned out to be concrete slag from when they poured the driveway. I was pissed enough to take more swings before I finally thought better of it and went looking for something more effective and less demonstrating my stupidity.
The ax sat in my garage shaming me for years until I decided to make it right again, hence all the YouTube research. I popped it in my vise, spent a lot of time with a file working out the damage I did to the edge and eventually got a decent profile/edge to finish with the Lansky. I hope the time it took me means I got a nice piece of steel in the ax rather than owning a crappy file.
It's a big one - 32"+, so not to long ago I got a camp-sized Husqvarna and a matching hatchet. I need to re-handle the old one, which has resulted in more research but no action yet.