This is a guide that details some of the best practices for hunting shiny Pokémon through soft resetting. This is the most common method used when hunting for shiny Pokémon that are only available once, such as legendary Pokémon.
A “soft reset” is when you restart your game without shutting down your entire console. In the DS and 3DS series of games, the easiest way to perform a soft reset is by pressing L + R + Start/Select (either Start or Select will work). The Game Boy (including Color and Advance models and games) can be soft rest by pressing A + B + Start + Select. Pokémon XD: Gale of Darkness can also be soft reset by pressing Start + B + X on the GameCube controller. Soft resetting in this manner will take the game back to the title screen immediately allowing you to just jump back in to your save file without closing out of the game.
In the most recent titles–Pokémon Sword and Shield, for example–this is no longer possible. You must press Home, close the game, and then reopen it.