Here's how.
I started with this modern axe. I probably should have looked for one with a slightly larger head that WASN'T painted black. Next time...
I removed the handle.
I took the head to the wire wheel on my bench grinder and removed most of the paint.
I then used the angle grinder you see here with a cut-off wheel. I ended up using about 50% of the wheel so that should factor into the cost of the ax. I get my angle grinder wheels from Harbor Frieght rather cheaply so the $5 ax may have cost about $6 when you account for the raw materials used.
I used the cutting wheel to get close to the shape you see above. I then spent about 30 minutes on the bench grinder rounding out and cleaning up the face.
I took the previously ugly and modern looking handle and shortened it a bit. I also removed some of the shape to it and made it a bit more comfortable for my needs.
I use this axe for cutting, carving and shaping so a short handle works very well.
Very happy with the finished ax. I keep it ground to a very sharp bevel. I wouldn't ever use it to cut a tree down or do serious hewing, but it is great for smoothing and carving. It is light enough and balanced enough that I can carve very nicely with it as you see here. I might polish it up more later, but I was eager to get it to use.
At the local Kane County Flea Market I found a couple really nice looking "vintage" axes. These were each $5 as well. One came with a handle and one did not. Well, it actually did have a piece of wood on it that the seller called a handle but I pulled it off and threw it away before I left. I was basically buying two ax heads for $10.
Both axe heads were vintage hewing axes. Both had a heavy poll which had bee slightly rounded from use. The poll allows you to strike the axe with another tool to help drive it through the log. I planned on grinding down the rough edge. I don't mind the rusted and aged patina on the axes, but I want to grind down any sharp edges or dings in the blade.
I chose a couple chunks of oak from the firewood pile that I would use for the handles. I planned on making one axe left handed and one right handed. A hewing axe has an edge ground on only one side so that it will cut the surface of the wood smoothly without biting in too deep. Since I am right handed I took the better of the two heads and planned on making that into my right handed axe.
The picture you see here is my "right handed" axe. If you are astute you will notice that I have mounted the head backwards. Doh! I was able to easily remove the head, cut a new wedge and remount it correctly. I didn't take another picture, but the finished ax is reversed. The flat side should be on the left side of the face as you look down the axe from the rear (poll) side. That way when the axe swung with the right hand it will smooth the material