Here is how you can unlock a secondary class in Tiny Tina's Wonderlands.
How to Unlock a Secondary Class in Tiny Tina's Wonderland
You will unlock a secondary class when you start the "Ballad of Bones" main story quest. This will become available around level 12. Upon unlocking a secondary class, you will be able to choose from the remaining five classes. You will immediately get access to their class feat and their first action skill. You will unlock the secondary action skill at level 18, and will have full access to their other skills from the moment you select the class.
You will be unable to respec, or change your secondary class until you have completed the main story, so chose your secondary wisely. From that point onwards, you will be able to select between your primary class and your secondary classes' active skills.
You can only have one of the four skills active at any time.