Most people cannot name the watershed they live in. It is one of the most useful pieces of local knowledge available, and tracing it is a genuinely satisfying afternoon project.
Start with the water you drink
In the United States, community water systems publish an annual consumer confidence report. It names the source, whether a river, reservoir, or aquifer, and lists what was detected in testing. Most countries have an equivalent disclosure. Reading it usually answers the first question immediately.
Trace the drainage
Public watershed mapping tools let you enter an address and see the drainage basin around it, along with the streams and rivers that carry water out. Following your basin downstream to where it eventually reaches the sea makes the connection between local runoff and distant water bodies concrete.
Find out where wastewater goes
Locate the treatment plant serving your area and the water body it discharges into. This step is often the most surprising part of the project, because the discharge point is frequently upstream of somebody else's intake.
Write it up
Two pages describing your source, your basin, and your discharge point is a complete piece of local research. It also makes every subsequent water headline more legible, because you have a specific place to attach it to.