Canteens can be acquired in three ways: (1) Airdrop crates will often contain canteens already filled with clean water. (2) Hunter Blinds sometimes have empty canteens, and (3) Very occasionally, killing a Zombie will result in an empty canteen being dropped.

In order to fill a canteen, stand in water, and look down. You will then be presented with the 'action' option (to press the "E" key). ALL empty canteens in your inventory will then be filled with dirty water.