The girl will awaken from her misadventure with the soldiers in a house in Narshe. Her rescuer, an agreeable older man named Arvis, reveals she'd been held in thrall by a slave crown - and discovers she doesn't remember anything past her name: Terra. Before Terra can do anything, however, two Narshe soldiers start pounding on the front door and demand she be handed over. Arvis insists you escape out the back of the house, but before you do grab the Elixir from the clock in the front hall. Be sure to check every clock you find in the game as they often contain items.
Head left across the bridge. You'll be spotted by Narshe soldiers, who set off in pursuit. Your path will lead Terra into the mines where she'll be at the mercy of the cave's monsters. Fortunately none of them are terribly strong, and Terra can easily dispatch them with either her Fire spell or sword attacks. Spend a bit of time leveling Terra while you can, as there's an easily accessible save point you can use in conjunction with Sleeping Bags found in the mine. Snag all the treasure boxes.
When you're ready, head north through the cave. Terra will get cornered by a squad of guards. Before they can grab her, however, the ground gives out under Terra and drops her into a new cave. After passing out she's subjected to a flashback dream featuring a crazed imperial man who pushes her into frying troops with her magic.
The game jumps back to Arvis, who has contracted a thief named Locke to rescue Terra. Locke's at first reluctant, but upon learning of Terra's helplessness decides to go ahead with the operation. He then leaps down beside Terra in the cave, just in time for a Narshe soldier and a horde of monsters to arrive at the far end.
Just as things look grim, however, Locke is saved by a group of moogles who offer their aid in his battle. You'll now have control of three parties which you can switch between with the touch of a button. The monsters slowly advance towards Terra, and you must use the moogles to block off access to her. The easiest way to clear this spot is to use Locke's group and the group without the moogle named Mog to clear out most of the enemies, and then send Mog in to fight the leader at the far end. (Be sure to let Mog fight at least once as he'll learn a Dance you can use in the fight.) With Mog's Dance command you can potentially eliminate the boss without having to deal a single HP of damage. No matter how you deal with the advancing squads, make sure they don't reach Terra or it's game over.
Once the boss is dead Locke will leave with the unconscious Terra in tow. She'll wake up during the escape, introduce herself and reveal her amnesia. Locke, a bit flustered, decides to take her south to the kingdom of Figaro and away from the belligerent Narshe militia.