There's a brief fishing tutorial the first few times you use your fishing rod (at least, I don't notice it any more, coming from someone who has already invested an unhealthy amount of their life in this game), but I found the first couple times I tried to read it, I got a fish hooked and was either trying to figure out how to keep them hooked, the instructions faded away too quickly, or the fish got off the line before the instructions could even fade. I've already stated my dislike for the current fishing system before, but there definitely also needs to be clearer instructions.
You want to move your mouse left or right following the arrow on the screen hovering above the fish - so when the fish is moving left, point your mouse left so that the fishing rod in the game is pointed that way. Same with right. That'll keep the tension from going too high (usually), but to actually reel the fish in, you have to left click. Reeling also increases tension, so mind the tension bar, and stop clicking if it gets too high. (At least, I think it's clicking and not holding; I stopped fishing early on because I don't like it, but also because it's just not useful; there aren't many fish, the cooked fish recipes aren't worth the effort for their low stamina regen, and the fish aren't big enough money earners to bother with. )