How to use: In order to get the class on the left, you must raise the Job Level of the required classes on the right. Example: In order to get the Knight job unlocked, you must attain a job level of 2 in Squire.
Squire – No Requirements
Chemist – No Requirements
Knight – Lvl 2 Squire
Archer – Lvl 2 Squire
Black Mage – Lvl 2 Chemst
White Mage – Lvl 2 Chemst
Monk – Lvl 3 Knight
Thief – Lvl 3 Archer
Time Mage – Lvl 3 Black Mage
Mystic – Lvl 3 White Mage
Geomancer – Lvl 4 Monk
Dragoon – Lvl 4 Thief
Summoner – Lvl 3 Time Mage
Orator – Lvl 3 Mystic
Bard* – Lvl 5 Summoner, Lvl 5 Orator
Dancer** – Lvl 5 Dragoon, Lvl 5 Geomancer
Ninja – Lvl 4 Archer, Lvl 5 Thief, Lvl 2 Geomancer
Mime – Lvl 8 Squire and Chemist, Lvl 5 Geomancer, Dragoon, Orator, and Summoner.
Onion Knight*** – Lvl 6 Squire, Lvl 6 Chemist
Samurai – Lvl 4 Knight, Lvl 5 Monk, Lvl 2 Dragoon
Arithmetician – Lvl 5 White Mage, Lvl 5 Black Mage, Lvl 4 Time Mage, Lvl 4 Mystic
Dark Knight*** – Master Knight and Black Mage jobs, Lvl 8 Dragoon, Ninja, Goemancer and Samurai, and turn 20 enemy units into crystals (kill said enemy and wait for crystal to appear).
* Job is Male Only
** Job is Female Only
*** New Job
Easy Level Up Method
You can do this at any point in the game, but I found it most useful in the beginning before going to Dorter Trade City for the first time. All characters should have the support ability JP Boost. Having a Knight makes it easier and able to last longer as well as having somone with the Monk abilities Chakra and Revive. The easiest battleground seems to be Mandalia Plain, but anyplace you like will suffice. Get into battle and kill all but one enemy. Surround the last enemy and proceed to use the Knight to Rend Power and Speed, effectively making the enemy weak.
You can also rend the power of your own characters to make it last longer (no surprise critical hits to end the battle early). Attack the enemy and your own characters to gain JP and EXP. Use Chakra and Revive where needed to keep it going. Usually a half hour to an hour of this will all but master a given job. If you want to raise an Arithmetician use the same method, but have Ramza and Luso in your party to use Tailwind on the slow mage. That way he will actually get a turn every round instead of once in a blue moon.
Kill Undead in One Hit
To kill any normal undead enemy just use a Phoenix Down on them. Chemists who can throw them make undead battles easy, if not somewhat costly.