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CardDAV is an address book communication standard that Google recommends using to sync Apple contacts. Enter google.com in the Server field. If you have 2 Step verification enabled (meaning you require a special code that is sent to your phone to log in), you will need to generate and enter an application specific password.  The switch next to the Contacts option should be green. Syncing will automatically begin.

Summary:
Open the Settings app on your device. Select Mail, Contacts, Calendars. Select Add Account…  Select Other. Select Add CardDAV Account. Enter your Gmail account information. Press Next at the top of the screen. Ensure that Contacts is switched on. Open the Contacts app on your device.