Fishing was the act of using a tool, such as a rod or fishnet, to catch a fish, often for the purpose of eating it. It was often done on camping trips. Among the tools used for fishing was fishing line. One who fished was identified as a fisherman.
A number of people were seen fishing near a parking lot when Dr. Gillian Taylor had a conversation with James T. Kirk and Spock in her truck in 1986. (Star Trek IV: The Voyage Home)
Ash Tyler kept photos of himself fishing from his childhood in his quarters aboard the USS Discovery in 2257. (DIS: "Will You Take My Hand?")
Doctor Joseph M'Benga enjoyed fishing as a hobby and took the chance to do it when he went on shore leave in 2259. (SNW: "Spock Amok")
According to the alien huckster in his sales pitch, "Nimbus III is famous for its plentiful local wildlife, and the fishing is terrific." (Star Trek V: The Final Frontier)
When William T. Riker was young, he and his father, Kyle Riker, went fishing in their home state of Alaska, where he hooked a salmon, but Kyle took the rod away and wouldn't let William reel it in, afraid that he might lose it. The younger Riker kept a photograph of himself holding the fish, despite not having caught it himself. (TNG: "The Icarus Factor")
Carl and John Torres were known for their lack of fishing skills. On one fishing trip in the 2350s, they brought their children who also went fishing, Elizabeth, Dean, Michael, and B'Elanna. (VOY: "Lineage")
In the 2360s, Jake Sisko and his father Benjamin went fishing at a pond on Earth. They brought a holoprogram of the pond to Deep Space 9 when Benjamin was reassigned there in 2369 and Jake played it aboard the starship they traveled there on. (DS9: "Emissary")
According to Neelix, "Well, genealogy's a lot like fishing. You've got to cast a wide net." (VOY: "11:59")
Presumably Charles Tucker III also enjoyed fishing, as his quarters contained a picture of him holding a fish.