I always find I learn programming easier when I am building some practical instead of going through various tutorials that you just throw away when you are done. So with that, my "learn Qt" project is something I'm calling qAndora:
qAndora is a cross platform, open source, Pandora Internet Radio client written in Python using Qt and VLC. If you would like to jump right to giving this little application a try you can find install instructions here. I have tested the player successfully on Ubuntu 14.04 and Windows 7, but it should work anywhere you can install VLC and run Python.
A few other random screenshots of the tool:
If you have any suggestions or feature requests please feel free to leave them in a comment below.