To the northwest of Baron is the town of Toroia, where Kain told you the Earth Crystal is located. There is a small piece of land to the right of the castle and above the town where you can land the airship. Land there, and enter the castle.
Speak to Edward
Go straight ahead, until you reach a room with the 8 women. Speak to them and they will tell you that the Dark Elf stole their crystal. Now leave that room, and go through the door on the left side of the next room. Eventually you will find Edward lying in bed. Speak with him and he will give you the TwinHarp, an item you will need in the Dark Elf's cave.
Leave the castle and go north. When you see a clearing with a small clump of trees, walk into the middle of it. Find a black chocobo and speak to it. It will allow you to fly across the river to the east, so that you can reach the cave where the Dark Elf is. Enter the cave.
When you enter the cave you find out that there is a magnetic field that makes it impossible to use metallic objects. You need to equip either Cloth, Leather, or similar items. Iron and Silver Rings should either be removed or replaced by Ruby Rings. It is also wise to hang on to Cid's Wooden Mallet until this dungeon has been completed, unless you plan to equip him with a bow.
When you first enter the cave there will be bridge to the east. Once on the bridge take the path to the south. Follow that path until you reach the staircase. Go down to the next level. In the next room go across the bridge, and to the left. Go down that staircase to reach the next level.
In the next room, there is a save point through the first door found in that room. After saving, continue on across the bridge to the south, and then across the bridge to the west. Go through the opening in the cave wall on that island, and finally through the door. In the next room, go to the next staircase immediately on the left.
In this final room go to the left, and there are a series of torches leading up to a door. Go through that door and you will reach the Dark Elf. Once in that room, speak to the Dark Elf and he will engage you in battle. You won't be able to fight him at this point and your party will be defeated.
If you visited Edward, the TwinHarp will play to dispel the magnetic field. Your party's health is restored, and you may now re-equip metallic objects before attacking the Dark Elf again.
When you attack the Dark Elf again, he will not be able to do as much damage as before Edward aided you. Attack it for a little while and it will turn into a dragon. This fight is very simple due to the effectiveness of the spell Weak. Have Tellah cast this spell, and the dragon will be down to only a few HP. One more attack and it will be dead. Now take the Crystal and leave the cave. Get in the Chocobo and it will take you back to the Chocobo forest. Walk back to Toroia Castle.
Kain Takes the Crystal
Return to the room with the 8 Clerics. An omnious darkness appears and Kain's voice will once again instruct you to bring the crystal in exchange for Rosa. The clerics will allow you to keep the crystal, and if you speak with some of them, you get permission to take the treasures in the basement of the castle (located on the right wing). These treasures include Dry ether, Remedy, High potion, Silver apple, Echo herbs, Elixirs, GreatBow, Thunder arrows, Ice arrows, and Fire arrows.
Go outside and board the airship. Kain will fly in with his airship and take you to the Tower of Zot.