I've an HTC Desire HTC (Android Gingerbread) so went to the Google Play Shop (was Market) to find and download the app. Easily found and installed (although the 2* rating didn't give me me much hope that it would be any good).
You run the app and log in with the email address and PIN you use to register via a web browser (see previous post). Again it's very dodgy from a security point of view with the PIN showed in clear.
Here's the main menu which shows the room structure that I previously set up via the web interface. Must be downloading it from the same place. The layout of the app is very poor with labels too big for buttons and in some places navigation buttons partially hidden behind other controls.
Click in to a room and you can see the devices you've set up in that room. Here are the buttons for 2 lights I've set up (wait for a later post on this). A "feature" of the app is that the only button that actually works is the top left one. None of the others actually function properly!
When you switch something off and on you get a confirmation message such as that below. Tells you it's worked but it's a bit geeky/techie, (good for the likes of me but perhaps not for the general populace).
I mainly tried this walking around my house but didn't have WiFi on so it was definitely using the mobile internet via my mobile provider (Vodafone). I did switch a light on when I was out and about and it was still on when I came home!