Companions level up simply by gaining experience points from killing enemies. You can grind your way to max level to unlock all the Companions features if you prefer this. The Mages Guild, Fighters Guild and Undaunted are unlocked by simply completing a daily from these Guilds. To level up the Mages Guild, Fighters Guild and Undaunted you will have to complete dailies for the guilds repeatedly till you reach the max level.

  • For anything related to grinding I do recommend reading the Grind Guide.