You can unlock talents by speaking to the Mighty Manager in Flarine.
Every job has their own set of talents to unlock.
Talent Points can be obtained by killing monsters. Every mob in Madrigal, Coral Island, Azria, Traseia or Dark Traseia has a low chance to drop 1 Talent Point.
Monsters in dungeons have a slightly higher chance to drop 2 Talent Points.
You can also get bigger amounts of Talent Points in Dungeons, from Giants or by competing in the Soul Challenge.
Talent Orbs are items dropped from Dungeons. They can be set into certain slots in your talent window and grant a level for a buff skill.