Fishing is the act of using a tool to catch a fish, often for the purpose of eating it. It is often done on camping trips.
A number of people where seen fishing at the Golden Gate in San Francisco in 1986. (Star Trek IV: The Voyage Home)
When William T. Riker was young, he and his father, Kyle Riker, would go fishing in their homestate 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 and his father Benjamin Sisko would go fishing in at a lake on Earth. They brought a holoprogram of the lake to Deep Space 9 when he was reassigned 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.