The new feature is found via the FAB when you open the YouTube app. Give it a quick tap, and you'll be taken to a screen from which you have the option to either record, as normal, or Go Live with streaming content. Make sure your account is verified, or you might not see it. There might be a roll out of some kind since it isn't on my phone quite yet, but our own Artem sees it on his.
If, for whatever reason, you don't have the app, download it over at Google Play or APKMirror and get to streaming. And remember, it might be live, but a little preparation might go a long way.