Oh, and since it tends to be the next question after this comes up:

To unlock an additional class, go to the Guildhall for the class you want to add and take a quest from the Receptionist there. This will unlock the class and provide a starter weapon or tool for the class. Your current class is determined by what main-hand weapon or tool you equip (and you have to unlock a class before you're entitled to equip that weapon/tool type). Levels are class-specific, so for instance, if you're a level 20 Thaumaturge and you unlock the Conjurer class, then when you first equip a Conjurer's wand, you'll be a level 1 CNJ.

Thaumaturge, Gladiator, Pugilist, Weaver, Goldsmith, Alchemist, and Miner guilds are in Ul'dah.
Conjurer, Archer, Lancer, Carpenter, Leatherworker, and Botanist guilds are in Gridania.
Arcanist, Marauder, Cook, Blacksmith, Armorer, and Fisherman guilds are in Limsa Lominsa.