The basic fishing rod is basically a scam, in that it’s almost impossible to catch anything but the most basic fish. The “natural rod” you can buy from vendor takes 2 out of the 3 stats on the basic from 2->4 for almost nothing. And some fishing spots have an upgraded rod already.
As for how it works: It’s basically like fishing with a spinner. You throw it out and slowly reel it in as they swim towards lure/bait, and you pull/click as they bite. Then you pull the rod opposite the direction it’s swimming and try to reel in a bit at the same time(if it’s swimming towards you, just reel). As the line turns from green to red, you stop moving and reeling in to let the line “cool down” before doing it again until it’s at the shore(I often recommend standing a little bit into the water if it’s shallow, since standing too far back will prevent catches)…
There’s also different bait depending on wherer you are fishing; Mountain lake bait wont always in a river.
And once you have a hang of the basics, there are two quest chains that give you high level fishing rods.
Maybe they meant the 1800s?