This guide was designed to detail all of the job classes in Final Fantasy III for the Nintendo DS. Hope it helps!

Freelancer	---	Your beginning job class. Not much to say about these except that they show your characters in their original outifts.
Warrior	---	Your basic swordsman. Have a pretty strong attack that, when combined with a good sword, can deal decent damage.
Monk	---	The first martial artist job that you can use. Claws are recommended at beginning job levels, but bare fists tend to be better later.
White Mage	---	A healing mage, a White Mage can use white magic up to level 7. Recommended to use to heal your characters.
Black Mage		An offensive mage. Can use strong black magic up to level 7 to deal varying damage. Can also wield a bow and arrow.
Red Mage	---	A multi-cross between a Warrior, White Mage, and a Black Mage. Highly recommended because it can provide a strong physical offense while still being able to heal and deal magic damage as well.
Thief	---	Thieves are fast and agile, and will normally strike first. It's Steal ability allows it to take items from enemies, and with a job level that grows faster than other jobs classes, can deal large amounts of damage with knives and other weapons.(Recommended)
Ranger	---	Not many people use Rangers, seeing as the damage they deal comes at a monetary cost by having to buy arrows. Nonetheless, Rangers deal the same damage in the back row and can be decently strong as well.
Knight	---	The Knight is a much more powerful upgrade of the Warrior. The Knight can use lvl 1 white magic(Cure spell), and has great HP progression and armor and weapon choices. Good choice for all the way up to completing the game.
Scholar	---	The Scholar is pretty weak compared to most other jobs, but it is highly recommended for a certain boss in the game, and items deal more damage when you have a scholar use them.
Geomancer	---	Geomancers use the powers of the earth around them to use different types of effects to deal damage.
Viking	---	The Viking is a strong warrior who can use powerful weapons to deal lots of damage. Unfortunately, it is not very accurate until higher jobs levels, but it may help kill stronger enemies.
Dragoon	---	The Dragoon is a great job choice. Why? It deals extra damage to dragons, wields powerful spears, wears excellent armor, and is almost required for a boss in the game. Excellent for beating the game as well.
Dark Knight		The Dark Knight wields katana swords to hurt enemies, prevents dividing enemies from dividing, and can use a cool skill called Souleater to attack every enemy on the field at the cost of a little HP.
Evoker	---	The Evoker is a beginning Summoner. It would be better though to wait for the Summoner job, plainly because it is much, much stronger.
Bard		The Bard uses harps to do many different things, including healing, dealing damage, and causing status effects. I wouldn't use it unless you have it at a really high job level.
Black Belt	---	The new and improved version of the Monk. Like the Monk, it would be better to just use your fists as your main weapon. Also, the Black Belt is the only job class to be able to reach 9999 HP.
Magus	---	The Magus is simply a stronger form of a Black Mage that can learn all dark magic spells up to level 8.
Devout	---	The Devout is simply a strong form of a White Mage that can learn all white magic spells up to level 8. Recommended to upgradeall White Mages to a Devout as soon as you get the last set of jobs.
Summoner	---	The Summoner can use 8 different beasts to deal huge amounts of damage. Although limited by MP, it is recommended.
Sage	---	The Sage can learn all spells, including summons, but the Sage has been proven to have many MP limitations, so it would probably be best to keep with just a Devout/Magus/Summoner instead.
Ninja	---	Probably the coolest job out there, the Ninja is usually the first to attack, and uses powerful katana to deal damage. It also has the Throw ability to throw items like the almighty Shuriken, which is almost a sure-fire 9999. Recommended.
Onion Knight	---	The Onion Knight is a bonus job that you may earn by doing a certain sidequest. Onion Knights are weak in the beginning, but at job levels 90+, their stats become incredibly powerful. Onion Knights can wield any weapon, wear any armor, and use any spell. Onion armor can only be obtained by killing powerful dragons though.