Follow these steps to Synchronize your gmail contacts with your device:
1. Open the Settings application on your device.
2. Select Mail, Contacts, Calendars.
3. Select Add Account...
4. Select Other
5. Select Add CardDAV Account
6. Fill out your account information in the following fields:
- Server: Enter "google.com"
- User Name: Enter your full Google Account or Google Apps email address.
- Password: Your Google Account or Google Apps password. (If you’ve enabled 2 Step verification, you’ll need to generate and enter an application specific password.)
- Description: Enter a description of the account (e.g. Personal Contacts).
8. Make sure that the "Contacts" option is turned to ON.
After you've completed setup, open the Contacts app on your device, and syncing will automatically begin.
Setting Google contacts as your default account
If you have set up iCloud, are syncing contacts from another account, or already have contacts stored on the device, you will need to select a Default Account.