I'm sure that every one of us has, at some point or another wanted a Fire Axe. As far as I can tell, there are 3 reasons.
1: A Functional Tool
For sensible people only, for example, breaking down a door to rescue some trapped childrens from...something, i don't know.
2: A Whimsical Toy
For stupid people only. I knew a guy who liked to use his axe to chop up bits of burning wood from his fires. He got quite a lot of nasty burns in places you don't want ANY burns by doing that. No, Just No... I don't know if he likes to do it anymore. I'd guess no.
3: For the Sheer Coolness
Which is why I want it!

Step 1: Step 1....Find the Stuff

Obviously, you can't grab a Fire Axe out of thin air, so you'll need to get the components for this wonderful device. You need:
1: An Axe
2: Some Fire, or;
3: SomeThing that can be turned into Fire
Obviously, you don't want to be walking around with a handful of incandescant pain. I reccommend 3, really.

Step 2: Step 2.....Combine the Stuffs

In this step, I shall detail the delicate process of combining the Fire, or its substitute (Meths), and the Axe.
Splosh the Meths onto the axe.
Easier than i thought.

Step 3: Step 3.....Begin Activation

OK then, Begin activation is a bit extreme, even for this high-tech project, but i really needed a cool name for this step.
Simply light the Meths on the axe. Perhaps if you put meths on both sides of the axe, it'd look cooler, though it tends to drool round anyway.

Step 4: Step 4.....a Confession

You were lied to! Oh noes!
I'll confess that this does work, and if you want some burning alcohol on an axe, this is your project. That said, the flame is very thin and blue, and didn't show up well on the camera.
"Hmm..." Thinks I. "What can i do to make this flame show up more...?"
Then i remembered that the luminous part of the flame, the yellow bit is comprised of particles of carbon in the fire. I needed to get some carbon into it. I solved the (admittedly tiny) problem by dipping a piece of rag into the alcohol i'd spilled on the bench earlier and balancing it on the other side of the axe, then taking the picture. At least this way you can see the flame.
In all, a fairly pointless project, unless you need to chop something in the dark (stupid). It's also good for impressing kids.