Shinies are ultra-rare Pokemon whose coloring is vastly different from other Pokemon of that type. Thy can occasionally be found via random wild encounters, but using the game’s Ally system is a much more effective way to farm for shiny Pokemon (named for the shimmering sound they make when they appear).
The Ally system occurs in battle when a wild Pokemon is injured. In an instance like this, they may summon another Pokemon to aid them in combat. When farming for shinies, this mechanic will significantly improve your chances of catching a shiny when an ally is called in.
In order to do this, you have to first defeat the Totem Pokemon, then wander into any wild encounters in the Alola region. While in combat with a wild Pokemon, they may utilize the Ally system and summon help. This ally is the Pokemon with the best chance of being a shiny.
To up your chances of catching one, you can use an Adrenaline Orb, which will up the chances of one appearing as well. But, it’s important you don’t knock out any of the Pokemon when you encounter them so you can keep the chain going. It’s also helpful if yo uhave a Pokemon that knows the moves False Swipe or Hold Back, because both of thes will drain a Pokemon’s meter to 1HP without ever knocking them out. It’s also recommended that you take plenty of health potions and Ether (or Leppa berries) to keep your own Pokemon’s health and PP up for these specific moves.