Having a M-DOT version of your website is not enough these days. Every website should have a responsive version of their website and it seems Google is encouraging that as well.
Google has also put together a beautiful guide on how to move your M-DOT site to responsive. From a user experience stand point it is also very necessary to have a responsive website, but Google publishing a formal guide about it makes it necessary for webmasters to consider it seriously if they have been neglecting it.
Google has also recommended that webmasters should do the switching before they roll out mobile-first.
While you can go and read the full guide Google has published, we are going to put down here some important points that you will want to remember:
1) Make sure to make your website responsive before the roll-out of Mobile-First.
2) If you are not a developer or don’t understand how 301 redirections work, we recommend that you hire a developer and have him 301-redirect all old mobile URLs to the responsive versions. Unfortunately, there is no fast way to do it, you will have to do it on per-URL basis.
3) Also setup rel=canonical on the responsive URLs.