What is the best method for catching Shiny Pokemon in Pokemon Moon?

The chance of encountering Shiny Pokemon is random, with a base chance of 1 in 4096, however this chance can be increased in a few ways.

• Shiny Charm - A Key Item awarded upon completing the Alolan Pokedex, which increases the chance to encounter a shiny to 3/4096.
• Chaining - You can use an Adrenaline Orb in SOS battles (where the enemy Pokemon calls another Pokemon to the battlefield) to 'chain encounter' the same Pokemon over and over again. According to Bulbapedia, a chain of 31 will increase the shiny chance to 13/4096

Of course, some Pokemon can't be found in SOS Battles, so you'll need to either encounter them without chaining, or breed for them. The Shiny charm still helps with breeding, as well as using the Masuda method.

If you're playing the Ultra versions you can also get (some, not all) shiny Pokemon through getting decently far in the wormhole minigame. The odds on this are broken down over here at Serebii.

Speaking from my own experience, I've had more luck with this than with shiny hunting via random encounters, SOS chaining or even breeding.