If you are going exploring in a place short on water sources, you should bring a waterskin with you to quench your thirst on the go.
Making a waterskin requires leather, which can be obtained from pigs, cows, sheep, and other wild creatures.
To drink from the waterskin, first tap it to put it in your hand, then tap the attack button to use it. (I don't know which of the devs came up with such a ridiculous setup!)
If your waterskin is running low, just go into a body of water to fill it back up again.