You need to travel to the Guild of the job/class you want to unlock, talk to the receptionist, say yes to the guildmaster, and he gives you a weapon.
Since FFXIV uses the Armory system, as soon as you equip a weapon for another class (like the level 1 one the guildmaster gave you), you instantly change to that class, no matter where you are.
It's nice in the way that it makes things pretty easy to do.
It's HORRIBLE in the way that you will never be able to have any other weapon other than a Great Axe on Marauder, Single-handed sword on Gladiator, Bow on Archer and what else not.
Never say never, I'm guessing down the road that they will have multiple types of weapons for each class. So if right now a two handed axe makes you a maruader, then maybe later you could equip a 1 handed axe or a 2 handed axe to change into one. Don't see why not.
Orrrr they could just make it so once you change into a specific job then you gain the ability to wield multiple types of weapons or vica versa have only class wield multiple types and jobs stay as one.