First off, do you think there's some button you need to click to synchronize? No. They should be synching automatically. If they're not, then you need to troubleshoot your configuration - perhaps it's as simple as a login issue.
You ought to have setup accounts like iCloud and Google in System Preferences > Internet Accounts. Start there. If Google is not setup there, I suggest you delete the current CalDAV account in your Contacts preferences, then add the Google account in System Preferences > Internet accounts.
Then there's another possibility - that the account is working, but you're not actually viewing the account by selecting it in the Groups sidebar. (If you're not viewing the Groups sidebar, enable it from the View menu.)