This page explains how to get the Shiny Charm in Pokémon Sun and Moon, which makes you more likely to encounter shiny pokémon.

Get the Shiny Charm

Catch all the pokémon in the Alola Pokédex (see the List of Pokémon Locations), then go into the building to the left of the Dimensional Research Lab, go up to 2F, and go into the GAME FREAK office and talk to the game director to get a Shiny Charm. Just by having the Shiny Charm in your inventory, you will be more likely to encounter shiny pokémon.