Welcome to the forums, Richard!
Thanks for the kind words, but the best stuff written on axes is here - just scroll down for Ed's post:
http://www.bladeforums.com/ubb/Forum18/HTML/000552.html
I've been meaning to put up a page of sharpening pictures for some time - so I'll make sure that I get to it over the next couple of weeks. I can't get to it sooner because I'm in the middle of working on some computer networks as well as my day job.
There's been some scepticism in past posts as to just what an axe will do. That's because very few people these days have used a properly sharpened one. That would seem like fighting talk around here - but I think I can illustrate with a story. When I bought my Hults axe it came with a sticker saying that it was unsharpened. Strange since it would cut paper! What they meant was that it hadn't been sharpened with a proper final profile. They'd just put on a final coarse edge so that they didn't ship anything blunt - I've no idea why!! Being impatient I went out and chopped down a few trees with the edge that came. It did just fine. After that though, whenever I went out into the bush to sit by the river and drink coffee, I would spend an hour honing the blade. Lots of sharpening hours later I figured I had a good edge profile.
The first tree I tried out on had to be a leaning alder. These tend to "barber chair" or split up the middle of the trunk unless you put in side cuts. Well I didn't - thinking that no way could the blade cut in anywhere close to the middle of the trunk. I wanted to see just how much further the first cut would bite in with the new edge - thinking in terms of 1/2" to 1". The result was many inches more, and the tree trunk split upward from the cut with a big bang. The good news is that I survived to feel stupid..
If you will lay a ruler on the blade at right angles to the edge you should see that your axe is really a hollow ground profile. The only places that the ruler will touch metal is where the handle goes through and the last 1/2" to 1" closest to the edge. All axes except splitting mauls will be like this.
With really good axes the thickness of the blade will actually be less just behind the cutting bevel to reduce cutting friction.
The concept in re-profiling rather than just sharpening the coarse bevel that is already on the blade is to think of sharpening with a really long file or stone so that as you hone down the final bevel, the file/stone is also almost touching the metal where the handle goes through. As you will see, even if you did use such a long sharpener, it wouldn't touch most of the blade because of the concave profile.
It sure is a long job to re-profile with hand tools so lots of people use a hand held belt sander used slowly and carefully so as not to heat up the blade. If you use hand tools the suggestion by Ed to use a guard is vital - the job is long and you will get tired and distracted.
The key concepts are that the whole 1/2" to 1" final bevel is honed, and after it is honed right to the edge, finer grit stones are used to polish it to reduce friction. It will be more understandable with pictures..
Such a sharp axe is used for splitting with a special technique. Just as the axe hits the block, it is twisted slightly to give leverage in splitting. This really does work - and otherwise the sharp blade will get stuck in wood with knots. It's also a very dangerous technique until you master it by hours of slow deliberate practise on small stuff.
A saw complements the axe in cutting stuff where the follow through of an axe would be dangerous - either to the user or to the edge of the axe.
I think that with an old axe head and some paint I can show what I'm talking about - I'll just need a little time. Once we have that everyone can join in and we'll have something that will make sense. Please be patient so that you don't end up with a poor job on a good axe.
