This wikiHow teaches you how to sync your Google account contacts with your Android device's contacts or address book.
Steps
Step 1. Launch the Settings app
of the device.
Step 2. Scroll down the menu that appeared to Accounts, then select it
It is listed in the "Personal" section of the menu.
Step 3. Choose the Google entry
If you have not yet added your Google account on the device, you will need to do so now by pressing the button + Add account, then choose the option Google and follow the on-screen instructions to add your Google account or create a new profile.
Step 4. Activate the Contacts slider moving it to the right
It will turn blue to indicate that the contacts of your Google account will now be synchronized with the device and will be accessible from the address book.