Fisheries just need to be in the water and they'll generate fish items every so often. It doesn't actually grab the fish entities out of the water, it uses scripting to determine the number of fish where they are.
Clicking on a fishery will show the pertinent info.
For anyone else who runs into this: Fisheries get a -20% debuff depending on how many other fisheries are in range. So if there's 5 or more in range, they produce 0 fish. This is included in the info window when a fishery is opened.
Latest version has a visualization to show that range.