Head west to trigger a scene with Cynthia and a fight with an enemy, RABBIT. Yes go and defeat it.
The Battle is not hard so I won't give its strategy.
After the Battle you will be given a little tutorial on Weapons.
Be sure to read it as it is quite helpful.
After that, head west. Here you will find a two way. Head west then north and a scene will kick in.
Yusis will automatically head north in the three way fork. Head towards the chest to get "Guiding Feather."
After the scene go south back to the three way fork and head west to exit the dungeon and enter the over world.
(In the Field Map you will encounter the same enemies you encountered in the East Breezing Woods. They are quite easy and can be Auto Battled, though do watch out for your HP.)