After becoming the Champion of Alola, go to Poni Island and continue the story until you get to Resolution Cave. Zygarde 50% Form should be there and you get to battle it and catch it. Another Zygarde in its 10% Form can be obtained from Dexio in the lab on Route 16. You can use the device in there to merge Zygarde 50% Form, Zygarde 10% Form, and the 40 Zygarde Cells in the Zygarde Cube you get from Dexio to get a Zygarde with the Power Construct Ability. This Zygarde will transform into its 100% Form if it reaches half health to lower in a battle.
Source: The Official Guide to Pokémon Ultra Sun and Pokémon Ultra Moon