Details: Obtaining Zygarde is one of the most unique, complex and cumbersome in terms of Legendary Pokemon in all of The Alola Region, really that ever has been in Pokemon Games. This all begins in Heahea City when Dexio, Professor Sycamore's Assistant, gives you the Zygarde Cube to collect the cells that create this Legendary Pokemon. These cells are scattered throughout the region, and it is these cells and the number of such that allows you to build certain Zygarde Forms.
As you collect more and more Zyagrde Cells, you can go to the Research Lab on Route 16 and try to construct Zygarde, or one of its given Forms. There are exactly 100 different cells to find in Alola, and the percent of cells you use at the research lab depends what Zyagrde you will get. You will also be able to separate the Zygarde you build, and though this will mean you will lose your entire Zygarde temporarily, you can always rebuild it with more or less cells.
If you have 10 Cells, you can build a Zyagrde in its 10% Form. This Zyagrde will be at Level 30, and it will know thee Moves of Safeguard, Dig, Bind and Land's Wrath. It will have the ability of Aura Break. This form's level increases (to Level 50) and moves change (Bind, Land's Wrath, Sandstorm, Haze) as you progress further in the game.
If you have 50 Cells, you can build a Zygarde in its 50% Form. This Zygarde will be at Level 50, and it will know the Moves of Bind, Land's Wrath, Sandstorm and Haze. This form, too, will have the ability of Aura Break. It was this form of Zygarde that was found in the Sixth Generation.
After collecting all 100 Zygarde Cells, you can build a Zygarde with its exclusive ability of Power Construct. (The the Zygarde will only be in its 50% form when created, however, still with the Moves of Bind, Land's Wrath, Sandstorm and Haze.) With this ability, Zygarde will be able to change between its 10% and 50% Form, as well as its Complete Form during Battle. In it's complete form, Zygarde experiences a great increase to its overall Base Stats.
(There are also five Zygarde Cores that can be found through The Alola Region, each allowing your Zygarde Forms to learn certain Moves, some of which are even exclusive to only Zygarde.)