Absent a canonical explanation, the mechanism for Zeal's levitation would most conveniently begin with a lodestone of some kind--i.e., a magnet--since that's what Laputa used in Gulliver's Travels. This simple premise is undoubtedly then given the Chrono touch by recasting the magnet as some other power source. This was done in the game: Thus, the floating power of Zeal came from the Sun Stone, and later the Mammon Machine.
The question of water is one that has intrigued me for years. Zeal is evidently above the major precipitating layer of the atmosphere, at least part of the time. We do not know if it ever passes underneath the clouds to replenish its reserves--although that is one of the most plausible explanations.
The issue here is one of scale: If we presume the water is teleported, as some of you have suggested, the energy costs of doing so become enormous to the point of prohibition. Given the very high rate at which water simply falls off the sides of the island, and also considering evaporative losses (which will increase at high elevations), it seems plausible that Zeal's entire water supply is replaced every few days or weeks. That would seem to rule out teleportation, or at the very minimum it would make the use of teleportation as a water delivery mechanism exorbitantly expensive from an energy standpoint. If you think of what it must take to teleport even a single person, and then imagine the amount of water on Zeal, you would quickly realize that, if the water were delivered by teleportation, then well in excess of 99.999 percent of all teleportation activity at Zeal would be devoted exclusively to water transfer. There would have to be enormous skygates at one or more lakes across the planet, constantly engaged in water replenishment. In short, if teleportation is the answer, then Zeal is orders of magnitude more sophisticated than we gave it credit for. I find it hard to accept that such a nation could have been credibly challenged by Lavos.
Thought's notion of atmospheric condensation visibly does not hold up. There is no way to condense enough water to make up for what is seen falling from Zeal. Now, it is an assumption that those waterfalls are consistent; it could be that Zeal had recently received a good dousing, and that ordinarily not so much water is falling off the sides. But if that were the case, then we're back to square one: What mechanism caused the dousing? No amount of condensation could do it, given Zeal's size versus its water loss--especially when considering the much lower absolute humidity present at very high elevations.
Another possibility raised is one of portal-type teleportation, whereby a portal is opened underwater and some of the water "falls" through it. A corresponding portal opens up in Zeal, and the water is pushed out of it by the weight of the water body. This solution, while elegant, is impossible, given that doing so would present a gross violation of the laws of thermodynamics, and would have the practical consequence of supplying Zeal with an infinite energy supply--thus contradicting Zeal's stated energy problems.
As improbable as it seems, I do find the most plausible solution to be that Zeal itself descends below the cloud layer at regular intervals, receiving copious amounts of precipitation which are then stored as liquid water from Zeal's own heat and the heat produced by the melting of frozen water. Perhaps Zeal itself does not descend; perhaps the cloud layer rises. This could be done by moving Zeal laterally to a location where the precipitating cloud layer is higher, either by the geometry of a given storm system, or by the geography of the planet.