With that, you can refill from a water tank on your land OR fill up for free without using your resources at any body of water on the map.
To do that, you'll want to head to the Tools tab of the shop, head to Animals, and find the liquid transportation tanks. Smaller pens/enclosures/coops will require you to provide water as well as food.
Whilst there is a number of differences in the approach you need to take to care for each individual type of animal, there are a number of general rules and expectations to have.