Leaving clay jars in shady spots alongside new roads was a strategy of Rome when it conquered Egypt and the like. Ordinarily the stations would have been maintained by laboriously filling them from some kind of cart, filled with jars of water, and drawn by some creature.
The Hadrianic road that was constructed in a vain attempt to link Antinoos, a short-lived town that emperor built as a tribute to his catamite, with ports on the Red Sea, may have only been used by the crews which constructed it. The watering stations survive here and there along its route.
Occasionally such stations have been found along the Mediterranean coast of the Sinai. Those may have been the handiwork of either the New Kingdom Egyptians, or of the Persians (or possibly the Romans, who probably borrowed the whole idea from that very stretch of road).
Fishing boats sustain their crews through the catch, plus whatever land-grown food they bring along. Eating cooked, fresh fish will provide water to those who eat them. Fresh fruit won't last long on an ancient fishing boat, so it was probably dried before sailing. Dessicated fruit would not solve the water problem, but rickets would have been prevented. Toting along bread would also help, but not help much -- there is water in bread. I'd imagine that wine and vinegar was important in this connection.
Another phenomenon that was understood was evaporation. Some kind of low-tech solar distillation was probably known, regardless of what one thinks of ancient transoceanic voyages. The surface waters of the seas are fresher than the progressively more contaminated layers beneath; rain was no doubt collected whether the mariners wanted it or not; and taking a quick trip to a river mouth on shore to collect water wouldn't have been a hardship most of the time.
One of the discoveries made by various ethnic groups living on coral islands is that scratching a hole into the "bedrock" with a bottom below sealevel will often result in a freshwater well. Probably an analogous filtration is at work, if the anecdote is true. I'd heard that tale also, perhaps there's something to it. A kinda lackadaisical search leads me to this:
"Clay jars like have highly porous walls. As water evaporates through the walls, the water that remains is cooled. Many Middle Eastern and Egyptian homes still rely on these jars to provide cool drinks."
http://www.adventurecorps.com/sadana/95report.html