Fishing was the act of using a tool to catch a fish, often for the purpose of eating it. It was often done on camping trips.
A number of people were seen fishing at the Golden Gate Bridge in San Francisco in 1986. (Star Trek IV: The Voyage Home)
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. (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")
Presumably Charles Tucker III also enjoyed fishing, as his quarters contained a picture of him holding a fish.