I currently reading "The Eagle's Conquest" a historical fiction novel by Simon Scarrow. In the book, the legions of Rome invade Britannia. I was just wondering where did these large armies get all the clean water needed to sustain itself.
Herodotus famously claimed that the army Xerxes led against Greece was so large that it drank rivers dry. When he describes their march west and then south through Thrace, Macedon and Thessaly, he repeatedly mentions rivers that were "reduced to a pathetic trickle" by the thirst of Xerxes' host.
This is all obviously hyperbole, but Xerxes' invasion did show that a supply of fresh water was essential to the functioning of large armies. It wasn't the Persians who ran into trouble with this - they were experienced in the fielding of huge expeditionary forces and had their logistics pretty well worked out - but the Greeks, who had never before raised armies on the scale needed to repel Xerxes' vast invasion force.
For the battle of Plataia, the decisive battle against the Persian invasion army, the Greek alliance had assembled a coalition force of over 100,000 men. This army and its camp followers and servants needed a vast amount of fresh water every day in order to survive the summer's heat. Initially, they would simply get this water from the Asopus river, which flowed between the Greek and Persian camps. However, the Persians realised they were doing this and stationed archers on their bank of the river to target any Greeks who came down to quench their thirst. The result was that the entire Greek army came to rely for its fresh water on a single well, the so-called spring of Gargaphia. With a battle line stretching for miles, men were constantly moving back and forth with water to make sure all the allies could drink. The Persians' next move was to send their cavalry around the Greek line to attack the men guarding the supply lines and poison the Gargaphian spring. Their success left the Greeks with no water at all for their vast host of thirsty men.
The commanders of the Greeks knew that their position had now become untenable. They decided to retreat to a new camp on a location called the Island (probably a tongue of land between two tributaries of the Asopus, though the place has never been securely identified). Their main reasons to do so were, first, that the Island would provide the army with a ready supply of fresh water, and second, that the ground there was too rough for the enemy horsemen to mess with it.
The chaos that ensued as the massive Greek army attempted to pull off a nocturnal withdrawal across broken ground was spotted by the Persians at first light the next day. The Persians saw their chance and attacked in full force. Yet their long, disorderly charge and the tenacity of the Greeks meant that the Persians were eventually whittled down and broken in prolonged melee; the result was final victory for the Greeks and complete annihilation for the Persian invasion force.
Tl;dr: Greece won its freedom by sucking at all parts of army management, including getting water.
It was rarely a problem for the Romans. They generally tried to keep their armies and camps close to water sources, but made due with foraging when necessary. Soldiers would typically carry a personal waterskin, but larger leather bags were frequently carried by pack animals and slaves/servants.
Who actually gathered the water changed depending on the time and place; sometimes it was a part of soldiers' daily duties (like in Gaul, where supply lines weren't the most reliable), but military slaves/servants, non-combatant "camp followers", or water merchants were often dedicated to that task alone. In some cases, water carriers were forced to travel pretty hefty distances back and forth, acting as a very vital part of the supply line in arid regions.
My source here is The Logistics of the Roman Army at War, by Jonathan P Roth
Local wells, streams, rivers, or any other source they could get their hands on. They would have also had stores of water from their onset as well as other provisions, in case that they could not find water (or food) for long stretches of time.
On the subject of wells; during the first crusade, the princes crusade specifically, the crusaders had been marching towards Antioch and were being fatigued by the lack of fresh water, as all the wells had been poisoned by the local defenders. The lack of water almost brought the crusade to an end, but they managed to find fresh water when they went to an area that had not been poisoned.