Apple has built features into iOS that make it easy to automatically sync contacts between iPhone, Google Contacts, and Yahoo Contacts. Set it up once, and contacts will sync automatically in the future.
How to sync contacts from Gmail to iPhone
Sometimes contact lists are stored in different locations, such as a computer’s address book and an online Google or Yahoo account. With iCloud and other web-based syncing technologies, the settings you need to sync your address books are all on your iPhone.
To sync Google Contacts to your iPhone, make sure your Gmail account is set up on your iPhone. Once you've done that, or if you've already set it up, follow these steps:
Open the Settings app from your iPhone's home screen.