The easiest way to breeding the most beautiful shiny Pokémon is to use the Masuda method. This method is basically breeding two Pokémon from different origins to increase the chances of getting a shiny Pokémon. All that’s left to do is to reach the number of steps needed to hatch the egg which you do by walking.
When you leave two Pokémon of the opposite gender or egg group (or use a Ditto) at the Nursery, the woman outside will be the person who gives you an egg. You can tell when she has an egg ready for you because her arms will be folded. Each egg will take up a spot in you party so you can hatch up to 5 eggs at a time.
Shiny hunting using the Masuda method has a 1/1365 chance of producing a shiny Pokémon. If you have the Shiny Charm then it triples your odds of getting a shiny to a staggering 1/455. Just keep on hatching eggs until you get your beautiful shiny Pokémon.
There are a few things that can help with the processes of Breeding Shiny Pokémon.
First: You’ll want a Pokémon with Flame Body (A Fletchinder from Route 8 of Akala Island can help with that). This will help eggs hatch significantly faster when you have one in your party.
Second: After you become champion head over to Heahea city and enter Game Freaks office. There you’ll be able to battle Shigeki Morimoto. After beating him he gives you the Oval Charm. The Oval Charm increases the chance of a Pokémon laying an egg.
Third: To decrease the egg hatching time further make sure to use your Tauros using the Poké Ride feature and hold down the B button to run. Doing so out in front of the Pokémon Nursery where the stacks of hay are will allow you to run in never ending circles without looking at the screen. The loop will end if you ride in one direction, so make sure you keep circling around
Lastly: The Shiny Charm. To get the Shiny Charm you’ll have to catch all the Pokémon in the Alola Pokédex, 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. This will also increase the chance of hatching a shiny Pokémon from and egg.