When you experience crashes, try to use "Run in Term(inal)" instead of the usual "Run". This will execute your Csound file in a Shell, and you may get error messages which helps you to find out the reason. (For instance a segmentation fault by Csound will by force crash CsoundQt, but should be visible in the Shell as "segfault" or similar.)
Another frequent reason for crashes or hangs are problems with the Audio or MIDI settings. Open the Configure panel, and have a look at the Run tab. Try to set the MIDI Input Device to none (also the Output Device), and uncheck Use Csound MIDI modules. For Audio, check whether the RT Audio Module is set properly (try portaudio if you are not sure). Set the Audio Input Device and Output Device to -adc (input) and -odac (output). See the Configure Doc Page for more info.
If you experience bad crashes and none of the receipes helped, try Help > Reset Preferences.
If the build-in Manual is not visible, go to Configure -> Environment -> HTML Doc Directory, push the "..." button and set the directory to where your Csound Manual is.
Sometimes for a new installation of CsoundQt, the keyboard shortcuts are missing. In this case, go to Edit > Set Keyboard Shortcuts, and click Restore Defaults.
The Examples Menu provides a complete introduction to Csound and CsoundQt ("Getting Started"). You will also find the complete examples of the Csound FLOSS Manual, the McCurdy Collection (adapted to Csoundqt) and many others.
Any example of the Canonical Csound Manual will open automatically in CsoundQt. Go to any page of the build.in manual, click on the .csd link (for instance "diskin.csd" on the "diskin" manual page), and the file will be loaded into CsoundQt as new tab. Just run it.