To catch fish for your farm, you will need a Fisherman's Hut.
Unlike the Lumberjack Cabin, the Fisherman's Hut cannot be found in the shop. Instead, a derelict Fisherman's Hut is hidden deep in the woods, to the northwest of your farm if you follow the stream north:
To unlock it, you will need to expand your farm all the way up there to include it - until it is inside your farm property. Once you have done that, you can click on it to renovate the ruins and use them.