After defeating the Elite Four and becoming the Champion of The Alola Region, you will actually be shown as scene with Zygarde moving about a cave. After seeing this, go to Resolution Cave found on Poni Island to find Zygarde waiting for you. This Zygarde will be in its 50% Form and will be fought at Level 60, knowing the moves Land's Wrath, Glare, Safeguard, and Dragon Breath.
After capturing this Zygarde, it can later be used with the help of Dexio and Sena on Route 16 to make another Zygarde with the Power Construct Ability.