For the first time in the game you have control of the airship and can travel anywhere you'd like. Your ultimate goal is to go to Narshe, talk to the Elder, then take Terra to the sealed gate, but since you won't have control of the airship for a while after this, this is a good time to complete some sidequests and take care of business.
If you go directly south to Jidoor, the auction house will eventually have two Espers available for auction, Zoneseek and Golem, and they will sometimes sell cure rings and cherub down as well. Make sure to have 10 to 20 thousand GP on hand if you want to be able to win an auction. Zoneseek costs 10 thousand GP, Golem costs 20 thousand. Head to Mobiliz, which is on the right side of the map, the one town near the Veldt. Continue paying to send letters from the soldier there. You may need to fight some battles or visit Maranda a few times to allow the new letters to show up, but do all that's available now. One unfailing way to get the letters to show up is to go around the building and talk to the guy who asks "Do you know about the serpent trench" and tell him "no" after it plays the little animation, a new letter will appear on the table. it's repetitive and boring, but it works!
When you're ready, head to Narshe to begin another sequence. When it's finished, go to the room with the treasure chests at the bottom right area above the cliff to run into lone wolf. Follow him all the way up to the cliff near where you organized your three parties earlier. After Mog tackles Lone Wolf, you'll have the choice of either saving Lone Wolf from falling and getting a Gold Hairpin which cuts magic use in half, or of saving Mog and getting him to join your party. Even if you don't save Mog you'll still be able to get him in the world of ruin, however, the only way to get all of Mog's dances is by saving him now, and you'll be able to get economizers later in the game which make the Gold Hairpin worthless. So go ahead and save Mog.
The secret to using Mog is that he has a dance available for each terrain type. Each dance technique allows Mog to continuously execute special attacks particular to that technique until the battle ends. When he attempts to perform a dance, if the terrain matches the dance he is attempting it will be executed for free. If the terrain does not match he will attempt to change the terrain which has a probability of success or failure. Whenever Mog fights in a terrain for the first time, he learns the dance particular to that terrain.
The next thing to try is collecting Mog's Dances. You should already have the Dusk Requeim if you used him to fight at the start of the game. Fight in a grassy area to learn the wind song. Fight in the forest to learn the Forest Suite. Fight in a mountain area like Mt. Kolts to learn the Earth Blues. Head over to the desert like the one near Figaro to learn the Desert Aria. Head to Zozo to learn a town/indoors exclusive dance known as the Love Sonata. One other dance, the Snowman Jazz, can only be obtained in snowy areas. Therefore, you can only get it fighting in the hills behind Narshe in the World of Ruin. The last dance is the Water Rondo, which is a tricky one to get but well worth the effort.
The only place you can earn the Water Rondo is in the Serpent trench, the path you took Sabin and company along during his scenario. You will need to drop yourself off using the airship, go down the trench and retrace his entire path to both get the dance and end up back with your airship. Drop yourself off at the cave to the south of the Veldt and remember where you parked. You'll need to jump down the Serpent Trench again and fight your way through WITH MOG so he can learn the water specific dance. You'll wind up in Nikeah. Head to the northeast and wind around the cliff. The path is now unblocked, and you'll reach the house where Sabin began his scenario. Take the same path you did before until you reach the mystery forest. This time the path which led you to the phantom train will just take you out. Head to Baran falls again and jump off, and you'll end up on the Veldt. From here just return to your airship, and you'll probably have fought enough to learn most of Mog's dances.
When you're ready, choose your party, including Terra, and give them espers. Head to the east part of the southern imperial continent and enter the Imperial Base (where you see a small house with a bridge next to it). Head to the mountain and grab the chests as you go, watching the timing on the room with the switching platforms. Flip the switch above the platform in one of the next rooms to create a bridge to a chest with a genji glove. Flick the right switch in the next area to fight a Ninja, flick the other switch to reach a save point. Flick the switch on the bridge to lower a staircase. At the bottom of the staircase there are 4 hidden treasures. The first is 1 step left of the stairs. The second is 2 steps above the passage going right. The third is 2 steps left of the slope at the bottom. The fourth is 4 steps above the chest. In the next room step on the first pressure plate but not the second, it will cut off a path. Flick the switch inside the chest. Make sure to hit the pressure plate at the lower left and open the room under the stairs to get some chests including the Atma Weapon, which will end up being the best weapon in the game, its damage matches your HP level.
Head through to the final room and Terra will try to open the sealed gate. You'll fight Kefka very briefly then the Espers will pour through and the gate will close. Leave, and there will be a shortcut out of the cave. You'll end up crash-landing on the imperial continent, pick whatever party you'd like and head back to Vector.