Upon reaching the world below, you'll eventually find the town of Gysahl. This town is famous for its Chocobo Stables, where you can rent a Chocobo to traverse the overworld quickly and avoid random encounters. Gysahl also sells Gysahl Greens, which are essential for calling Chocobos in specific locations. Your next destination is the Gulgan Gulch, a small cave where you'll meet the wise Gulgan Elders. They will teach you the Toad spell, which is necessary to progress through certain areas.
The Gulgan Gulch itself is not a dungeon, but rather a narrative point. After learning Toad, you'll need to use it to enter the next major dungeon. Ensure you have a White Mage or a character with the ability to cast Toad, as it will be crucial. Stock up on items in Gysahl, as the upcoming dungeons are significantly more challenging than what you've faced so far. Consider experimenting with the Thief job if you unlocked it, as its Steal ability can yield valuable items from enemies.