Must be a small axe head.
Can be equipped to a 2h or 1h grip, but must be small axe head, I usually use 2h myself to make it, in my mind, the most like a fire axe or woodcutter's axe kinda deal.
2 ingots.
If you have no axe equipped, you should be able to just equip it while on any slot, but if you do have one equipped, you need to select the corresponding tool's slot to equip a corresponding tool (said this way as it applies to all tools and their upgrades)