To unlock a job, there are a few pre-requisites:
1. The "main job" must be level 30
2. The "sub job" must be level 15
3. All main job quests must be completed

If these three conditions have been met, a new quest will open up. This quest will unlock the Job.

Level Conditions:
Bard = 30 Archer, 15 Pugilist
Summoner = 30 Arcanist, 15 Thaumaturge
Scholar = 30 Arcanist, 15 Conjurer
Dragoon = 30 Lancer, 15 Marauder
Black Mage = 30 Thaumaturge, 15 Archer
White Mage = 30 Conjurer, 15 Arcanist
Monk = 30 Pugilist, 15 Lancer
Warrior = 30 Marauder, 15 Gladiator
Paladin = 30 Gladiator, 15 Conjurer