This tutorial explains how you can take backup of your android phone contacts to your Google account. After sync, if you add a contact on your device, it will automatically get added to your Google account and it works vice versa.
Similarly, if you delete a phone contact it will automatically get deleted from your Google account.
You can access your contacts from apps icon in Gmail or you can access them from www.contacts.google.com.
Tutorial also explains troubleshooting steps that you…