For a complete guide on adding Gmail to your iPhone Please follow the instructions on Google's Support page HERE
You can also follow these instructions: (This is JUST for contacts)
- Open the Settings app on your device.
- Select Mail, Contacts, Calendars.
- Select Add Account.
- Select Google.
- Fill out your account information in the following fields:
- Name: Enter your name
- 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).
- Select Next at the top of your screen.
- Make sure that the "Contacts" option is turned ON. The switch should be green.
- Select Save at the top of your screen.
After you've completed setup, open the Contacts app on your device, and syncing will automatically begin.