Despite looking like any other town on the world map, Zozo is a rather unique experience. Not only is the place filled with liars and brigands, it's also home to countless random battles wherever you go. As such it's important to save before you go anywhere, since the enemies are pretty tough for this point at the game. Be especially wary of the Hill Gigas's and Veil Dancers, as the former has a strong earth attack and the latter uses powerful -ra magic.
Your first stop should be the Inn in the north of town. You'll find a clock embedded in the wall that needs to be reset. This clock actually forms the crux of a rather large puzzle encompassing all of Zozo; when it's set properly the clock will open a passageway to the powerful Chainsaw, one of the best Tools Edgar will ever get in the game and an excellent method for mauling bosses. Since every person (save one) in Zozo is a liar, you'll need to talk to them all and sort out their lies about the time to discover the real time. This is fun, but it can take a while since Zozo is huge.
(If you want to skip this lengthy puzzle, the proper time is 6:10:50. Whether you want to do the puzzle or not, however, GET THE CHAINSAW.)
Zozo looks pretty confusing, and given how many buildings there are it can be as there's only one you need to enter to progress to your destination. Go to the Relic Shop and you'll discover from the guy at the counter that there's no girl at the top of the building, which given their lies means that there's quite definitely a girl at the top of the building. From there you just need to keep climbing the stairs you find to the top of the building, moving past the line of liars until you find your way outside.
The outside of the building can be a bit confusing at first. You need to follow the cue of the building jumpers and leap from one building to another by going out the windows. Continue climbing in this manner and enter any doors you find (check them all, as they sometimes contain treasures you'll want) and you'll eventually find your way to the top of the first building. A man (actually a palette swapped Vargas) stands in your way, and though he offers to let you pass you'll be forced into a fight.
Dadaluma looks tough and can make himself even tougher by summoning iron Fists to help him, though this fight is a cinch with strong fighters. Edgar should use his Chainsaw, Sabin a Blitz, Locke attack, Cyan Dispatch, Gau a strong Rage like Bomb, Celes her magic and Shadow his shurikens. You'll know you're nearing the end when Dadaluma outfits himself with a series of buffs. Keep pummeling him and he'll go down quickly. The only attack you really need to watch out for is Dadaluma's version of Throw which can do hefty damage to one character.
With the faux friendly gone you'll have access to the sole safe room of Zozo - which, unsurprisingly, contains Terra. She's watched over by a strange man named Ramuh who reveals himself to be an esper, explaining the history of his people simultaneously - and asking for the team's helping in liberating his friends from the Empire. You'll agree to do so like the heroes you are, and Ramuh will grant your team a fabulous new option: equipping magicite. Looks like it's off to the Empire.