After Vicks/Biggs and Wedge find the frozen esper, the girl wakes up in a bed in a house.
Escape the House
After a cut scene, go to the right and talk to the man standing beside the bed. When prompted, name the girl. The default name is Terra. After the next cut scene, check behind the clock to find an Elixir. Then follow the man to the door. Go north through the door, then go west until you enter the mines.
5. Repo Man/Bandit
In the mines, use the Fight/Attack command against monsters during battle. You can use the Cure spell to heal, unless you run out of MP.
Go northwest. You will pass by a save point. From the save point, go north across the bridge. Ignore the chest to the right (and ignore all chests here) because you can get better items from them later if you leave them alone. Continue going northwest until you have crossed the second bridge, then go northeast. Eventually you will see a door, but the guards will arrive. And then you will fall.
After this, there is a flashback. Then you meet a new character (default name: Locke).
Locke finds Terra, then some Moogles appear. Press Y to switch between groups. First, have Locke's group and Kushu/Mogsy's group block the two paths to Terra. Then have Mog's group go through at least one battle, then have him go straight to the bottom of the area and talk to the guy there. You will fight the Marshal/Guard Leader.
Have Mog use Dusk Requiem/Twilight Requiem. If he stumbles, just keep trying. The other members of the party should use Fight/Attack, and use Tonic/Potions or Potion/Hi-Potions if necessary.
After the battle, you will leave the mines automatically. When you're outside, talk to the guy in front of the house, and go in. There is some recovery water in the bucket where you first come in. Don't open the chest in the rightmost room unless you want to fight a Lobo/Silver Lobo. Instead, check the pot there for a treasure. There are treasures in the other rooms, too.
After you are done in Narshe, go south to leave town.