One of the ways you can claim rights to water sources is to own land next to them or over them. It seems intuitive that you should be able to dip into a river running along your property to get a drink for yourself and possibly your livestock or water for your plants and possibly your farm fields. That works so long as you don't hog too much of the river flow and your downstream neighbors can do the same as you are doing. In practice there are so many humans today demanding so much water that the amounts each person or enterprise can withdraw are usually regulated by agreement or law.
The same goes for groundwater since aquifers rarely span just one person's property and can be very large, for example, the Ogallala aquifer which lies below 122 million acres of the U.S. Great Plains.
What is not so intuitive is that water rights can belong to people far from the water itself and that the rights to that water can be traded like any commodity. That's what residents of the Neches Trinity Valleys Groundwater Conservation District in the middle of East Texas discussed recently and quite heatedly in a public meeting of district officials.