Simply click on a dungeon's name to 'explore it', and progress the exploration percentage. You have a very high chance of encountering an enemy, which must be defeated in combat (or defeat you!) before you can continue. You still gain some exploration percentage even when you get an encounter, but less than if you manage to explore uninterrupted. Turns are taken in order based on the characters' AGL stats. The player who lands the killing blow gets XP, and levelling up grants +1 maximum HP.