Be aware that the only two handsets that support this at the moment are this Edge+ (not even the non-plus Edge) and the newly released G100. More will be along apparently, but if they're going to approach it in the same way as Samsung have done, it won't be a low-end addition - rather flagship or at least high-mid range. Who knows, though - maybe Moto will lead the way in making this low-end in time!
I tested this here with my TV and also a stand-alone monitor with bluetooth keyboard and mouse. You plug in a USB-C to HDMI cable between your monitor/TV and the phone and then pair up the keyboard and mouse to the phone (remember that phone remains the brain here) and fire up the software - or in this case, it fires up itself, offering a 'dashboard' of four big buttons to choose what 'group' of services you might want to use.
Each of these apps can then be controlled on the bigger screen, jumped between, tiled, resized, whatever you like really - just like a Microsoft Windows environment. The Notifications offers you a quick always-present item to turn your phone into a trackpad (just like DeX) and if employed, can be used as just that - if you have no mouse. Single tap to locate, double tap for execute, swipe to move cursor, two-finger swipes to scroll, two-finger press for context-menu, pinch to resize photos and so on. Just like most hardware trackpads.
Across the 'dock' at the bottom of the screen there's an App Drawer button, Home, Recents and Search on the left, then an array of 'control panel' stuff on the right - information and (generally) links to the Settings inside the phone - and on the far-right, an echo of the Notifications panel on the phone. The phone can be controlled in many ways from this setup including 'phone' and SMS via Messages. Uses the phone's speaker (unless your monitor has this functionality).
Turning to the TV, these big buttons might be a little more useful as you can obviously see them from further away and select with the 'trackpad' on the phone's screen. I was running films and video from my phone on the TV and the sound was routed through both my Roku Streambar and the phone. The latter can be hooked up with bluetooth so headphones can be used but beware of lip-sync issues and choose your app/bluetooth gear wisely! You can also call up gaming or Video Chat apps in the same way but unless your TV has a camera, it'll obviously use the camera on the phone. I didn't have a bluetooth gaming controller to test here but I'm reliably informed that this works well.
The 12GB RAM they stuffed into the Edge+ certainly enables switching between and running multiple tasks fluidly and provides for a powerful interface supported by the SnapDragon 865 chipset in the engine-room. The whole system is very much like DeX, which Moto have clearly based their model on. And that's not a bad thing - as DeX works very well for those who need it.
I'm not sure that we're there yet and all this feels, frankly, like a bit of a playground for nerds and geeks, but it is certainly great to see another OEM getting on-board with the idea and making it work so fluidly. Anyway, there's a quick overview of initial findings from first play. Please do feel free to ask questions and I'll try and fill in the gaps as I learn. In the meantime, there's a good video on YouTube demonstrating much of this if you'd like to take a look by Tim Schofield.