Frimelda
By following a chain of quests starting with "Under the Weather" (B4-07) and ending with "The Way of the Sword" (B5-11) the female paladin turned zombie will join your group. She looks and acts as a Hume (can go into any Hume class) and comes with some basic paladin action abilities and the Dual wield passive ability.
Monteblanc
Monteblanc can be unlocked by completing the quests; "Camoa Cup", "Graszton Cup", "Moorabella Cup", and "Fluorgis Cup". Then, there should be a mission available called "Wanted: Friends, Kupo". Do it, then you will unlock the moogle montebanc, who is a black mage class. He knows the full black magic set.
Al-Cid
Al-Cid can only be unlocked after the game has been completed. Then there should be a mission called "A Refined Recruit", and Al-cid will join your party. Al-Cid is a hume Agent, and can only learn Reconnaissance.
Penelo
Penelo can only be unlocked after the game has been completed. Then there should be a mission called "An Elegant Encounter"
Vaan
Vaan can only be unlocked after the game has been completed. Then there should be a mission called "Where Could He Be?"