I'm not sure I understand what you are asking. From Google's perspective, to shut down the API is simple: they just need to stop serving the requests they get to the API and that will shut it down.
If you are asking how to responsibly shut down an API, that is a hard thing to do. Having the API start failing intermittently a bit more than a month after you announce it won't be supported any longer is definitely not the right way to do it though. Giving people plenty of advanced warning is the least you can do, even if you technically _can_ shutdown the API whenever you feel like it.