You can take a fishing class for $400 to start the skill, or you can just start fishing. This is not a skill that you can learn from the basic skill books. (However, there are books you can read to learn how to capture specific fish. Frankly I think these are kind of a waste of money, since your Sim eventually learns how to catch those fish on their own.)
Fishing is not a particularly productive way to make a living. But you can tell your Sim to go fishing, and they will fish until their needs drive them to cancel the action. So it has that going for it!