1) On the iOS device, touch Settings.
2) Touch Mail, Contacts, Calendars.
3) Touch Add Account.
4) Touch Exchange.
Note: iOS 4.0+ allows multiple Exchange™ accounts. However, if you're on a device that doesn't let you add a second account, you can use IMAP to sync Gmail, CalDAV to sync Google Calendar, and CardDAV to sync contacts.
5) Enter the full Google Apps email address and a password and touch Next.
6) In the Server field, enter m.google.com.
7) Leave the Domain field blank.
8) In the Username field, enter the full Google Apps email address.
9) The password should already be in the Password field, if not, enter it again and touch Next
Notes about passwords:
Be sure that you have a strong password for your Google Apps account.
If you see an error message saying "Invalid Password", you may need to unlock your account by solving a short CAPTCHA challenge-response test. Go to https://www.google.com/accounts/UnlockCaptcha to allow access.
If you are a 2-Step Verification user, you should use an Application-specific password instead of a regular password in this field.
10) Select the Google services you want to sync, such as Mail, Contacts, and Calendars, and touch Save. To receive and respond to meeting requests on your device, you need to turn on Mail and Calendar here and New events in the Google Calendar settings. See Customize Mail, Calendar, and Contact settings for more information.
Starting synchronization: If Push is enabled on your device, synchronization will begin automatically. You can also open the Mail, Calendar, or Contacts app and wait a few seconds to start synchronization. If you recently signed up for Google Apps for Work, Education, or Government, it can take up to 24 hours before synchronization occurs.
Also Refer:- http://www.igeeksblog.com/how-to-sync-gmail-contacts-on-iphone/