Ambarish Kenghe, Chromecast Product Manager, writes:
To start mirroring, simply select “Cast Screen” from the navigation drawer in the Chromecast app and select your Chromecast device. On Nexus devices, this feature is also available through the quick settings menu.
It's in beta, and Google says "it will roll out on popular Android phones or tablets from Samsung, HTC, LG, and others over the next few days". The thing to check for is version 1.7 of the Chromecast app on Google Play.
To be precise, it is available on Android 4.4.2 (KitKat MR1)
It's always worth checking reveries of course, and one user comments:
5 stars now that screen mirroring (Cast Screen) has been added. Like another user has said, after initially connecting using Cast Screen, you may need to reboot your Chromecast device for mirroring to completely work properly. For me, sound wasn't working when I played video at first. But after rebooting the Chromecast, the sound worked.