This guide was taken from macworld UK. I'll paste the steps to take below, you can also click the link to visit the full guide in it's enterity. Essentially though you're going to have to login into your IPhone with your google account that the phone is attached to.
Open the Settings application on your iPhone.
Select Mail, Contacts, Calendars.
Select Add Account...
Select Other
Select Add CardDAV Account
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).
Select Next at the top of your screen.
Make sure that the "Contacts" option is turned to ON.
