Unlike prior games in the series, the player cannot use the fishing rod from the Bag menu — instead, there are rippling spots on bodies of water that can be interacted with by pressing the 'A' Button. If the player presses the 'A' Button again in time, the Pokémon will be reeled in and the battle will begin.
The Fishing Rod only comes in one model, which is obtained at the start of the game. It cannot be upgraded like in previous games of the series. The area where the player is fishing will determine what type of Pokémon is caught and the rarity percentages are determined in the same way as normal tall-grass encounters.
Fishing at the same spot repeatedly can increase chances of encountering Brilliant Pokémon and Shiny Pokémon.
Via Bulbapedia
Fishing spots are static in the game; they're always in the same location. They go away if you go too fast but other than that, they're pretty much always there. Walk away and come back a bit slower. You just have to know where to find them.
If there's something I'm missing, please let me know so I can edit or hide. But I hope this answers your question!
