If you're a Night Elf, you won't start with the ability to use axes. You'll need to go to Ironforge and pay 10s for the ability (proficiency) to use 1H Axes. The
Weapon Master there can teach you.
Once you learn the weapon proficiency, your
Weapon Skill with 1H Axes will still be low, and you'll want to kill some low level monsters until it increases.
If you're going to head to Ironforge, it might be a good idea to take the Tram to Stormwind and learn some more weapons there. (Or you might ignore me and save some money).