To upgrade your secondary class you gotta earn xp. It'll go towards your subclass and armor and weapon upgrades and after level 20 towards a mote of light. You can change out your subclass as easy as changing guns or armor but obviously can only have one equipped at a time. Fun fact tho: now that you unlocked the second subclass, if you decide to make a hunter or Warlock you can start out immediately with either subclass.