Alrighty, if you download the app and hit “menu”, you will get to some instructions showing you how the data is being sent. It does not seem too complicated. For the joystick or tilt, it sends out 4 bytes.
First byte direction of X
Second byte proportion of X
Third byte direction of Y
Fourth byte proportion of Y
The buttons seem to work in a similar way. Your UNO will recieve these bytes via a bluetooth unit of some kind (BlueSmirf etc). From there, it is simply a matter of writing some code to do something based on the value(s) of these bytes coming in.
I don’t know if that is helpful at all or not --“How do I do it?” is a bit open-ended. I am not sure if you need help with the data transfer protocol, the hardware, or code. --Also, it looks like the free version of this app will not transmit data. I think you have to drop the $1.65 on the “pro” version.
BTW --If you would like to try my app (which does more and (I think) is set-up much better), just zap me an email. I will be happy to send you a copy for free.
I have ordered the bluetooth version, which will probably work with other arduino based bots. The android side is not yet in development, but worth keeping an eye on.