How to sync your Gmail/Google Apps Contacts

I have tested this with iOS and Mac OS X 10.8

Go to where you would setup your contacts.  For instance in OS X you would open the contacts app and go to add account.

For iOS you would go to the mail, contacts, calendar section.

Click new for both.

Select Add CardDav Account.

Server: google.com
Username: username@gmail.com (or this can be your google apps account)
Password:  enter your password (if your using 2-factor authentication, you need to create an app password)
Description: Whatever you want

The Contacts App takes a few minutes to sync but the iOS app should be instant.

Source: Link