Hunter-gatherers generally stayed near water sources and probably knew how to get water from plants. Cities in classical antiquity and in some cases before had drinking fountains everywhere. My question is, how did the people who didn’t have these two sources of water stay hydrated all day? For example: middle ages, early agricultural societies, military and hunting expeditions etc. Did people walk around with bottles all the time like at modern music festivals? Or just drink a lot in the morning and evening?
Cities in classical antiquity and in some cases before had drinking fountains everywhere
And so did the Middle Ages! I have an overview on the aqueducts of the Medieval Period, and you'll note the great pains they took to ensure that the fountain water was Not Fucked With.
Yet the aqueduct is hardly the only source of water. Squatriti observes: "Indeed, only modern Western communities rely on a single source for water; all other human societies hedge their bets and simultaneously draw on numerous sources and types of water for domestic use."
We can see this in the case of Exeter, besieged in 1549 and 1643, in both cases with the attackers cutting its multiple conduits and melting down its lead cisterns and pipes for use as shot. Yet Exeter was well-supplied with natural water sources, and so whilst losing its aqueducts was a blow to the city in both sieges, it wasn't a mortal one. Same deal for Naples and Rome during the Gothic War of 535-554: Neapolitan wells were apparently sufficient to keep up with demand when Belisarius cut the supply, while Rome lost only its mills and baths, with even those people distant from the river able to draw on their supplies.
So what sort of natural water sources did they have? Rainwater is always an option, collected by gutters from roofs and paved surfaces and channelled into cisterns. And springs, and well, wells. (I still regret that my family moved away from the first house I remember us living in, which had an actual well with rope and bucket just outside, before I was big enough to draw from it. Ah, well.) The local conditions might make one type more preferable than the other - in communities on top of hills, for instance, or near marshes where the groundwater was especially salty, rain cisterns were more common than wells.
And, honestly, just rivers in general. From water does all life begin, saith the OC Bible. If you're on a farm, you can simply just dip into the same water you're irrigating with, as u/sunagainstgold points out. The Medievals concerned themselves greatly with the purity of their water, and if said irrigation channel carried water that was clear and non-odorous, your average Medieval person wouldn't hesitate to dip in and drink.