I find this website a great place to start http://zetcode.com/gui/qt4/
It basically provides short tutorials on a number of topics, which are self-contained and really easy to follow. I learnt Win32API GUI programming this way, and GTK. From trying out what I want from the tutorial, I then start looking for what do I want to do that's not in the tutorial? Google and sites like this then become my best friend...!
Start small - how to build / link a basic window in Qt. How to add things to it. How best to organise files etc. Then build up to what you want. Break the problem down.
I usually go by hand to start off with, with everything. This is because IDEs (Glade, Eclipse, NetBeans, Visual Studio) tend to generate a whole lot of code that I never understood as a beginner.
Edit - with the above tutorial, if you are on Linux, ignore the download bit in the tutorial and just go for the version of qt4-devel in your repositories.