How do I reverse "sync turned off" in my Google account? Under the Settings -> Accounts -> Google, there's an account in the Accounts section and under that it says "sync turned off."
When I tap on it there is a list of services that can be synced (e.g. App Data, Calendar, Gmail, Google Play Books, etc.) and I can manually tap one of those to sync it now.
How do I enable automatic sync?
I don't see any option to "sync automatically" (only "sync now") from within the account nor from the Google Accounts page.
It used to sync automatically, and I'm not sure what happened or why it doesn't anymore.
How do I get that back?
Go back to the Settings menu, and in the Wireless and Networks section tap Data Usage.  Then press the menu button and in the popup menu check the Auto Sync Data box.  

You can then return to the Google account page mentioned in the question, where the list of services is, and select the newly visible checkmarks next to which ones you want to automatically sync.