The goal is to have a large team of advanced champions that can face any situation.
Perhaps the most common means of adding to your team is to call forth another champion through "cashing" Shards at the Portal in the Bastion.
But one must also develop the champions one has. Champion Development involves:
Leveling your Champions
The Experience (XP) required to level up your champions comes primarily though Campaign Battles, though Experience can be gained in somewhat less energy efficient battles in the Dungeons and slower still in battles in the Clan Wars that cost you no energy but do require another limited resource Crypt Keys.