You have to use the fishing rod to catch 10 fish. These fish can all be the same species, and can all be caught from the same spot.
You unlock the fishing rod early on in the game by completing the quest "Fuel the Revolution". Once you have it, you can equip it using the weapon wheel. You can fish in any body of sea water, but there are certain spots that spawn fish in abundance.
Fishing itself is quite simple. You cast with RT, the longer you hold the farther it goes. Reeling the line in slowly (LT) will attract fish to the bait. When a fish takes the bait you will be prompted to hook the fish (RT). Then you will need to reel the fish in (LT) while fighting the fish by holding the LS in the opposite direction the fish is going. Once it gets close enough, you will catch the fish. (Tracker updates at this point).
There are several things you can do to make fishing easier, but none of it is necessary. You can build a fishing hut in one of the guerrilla camps. This allows you to buy maps of fishing spots and unlocks gear you can equip to make it easier to fish. At these aforementioned fishing spots there will also be tackle boxes that allow you to mod your fishing pole (similar to weapons at workbenches). These mods give additional bonuses that make it easier to fish.