So there are two fighting paths. You can either do guild quests, or you can explore (the compass icon). Exploring is the only way to find dungeons. The game does a random check every morning that you are exploring to see if you found a dungeon, and every time you don't find one, your percentage chance goes up.
Once you've found a dungeon, the game records the date, and you can enter that dungeon on that date (+ or - 5 days) in future lives.