Qt training tips and tricks
Get C++ GUI Programming with Qt 4, (the official Qt book) and start reading!
At first you should understand the signal/slots concept, because that is used heavily in Qt. Then I would work through some simple examples, there are lots of them, so just pick the ones you like. If you use Qt Creator you have the context sensitive documentation always at hand, which helps a lot.
If you think you know the basics you can concentrate on the more complicated things like threading or network communication, depending on what your company focus is.
Remember the Qt is not only the GUI framework, but has a framework for a lot of lowlevel components, too. Have a look here to get an overview.