Hello and welcome,
Hangs while joining are most often DNS related. While it is not strictly required/enforced, it is a good habit to always manually enter the first DNS server (the IP of your DC Master) and to always enter the fully-qualified hostname (hostname with domain) when you're asked to choose the host name of the system to be installed.
Another common cause of confusion can be the presence of multipe DHCP hosts in your network. The Univention Installer will try to get its first network configuration by DHCP. This will only succeed if your DC Master is the only host advertising DHCP. A ridiculous way to avoid that would be to disconnect the network until you're forced to enter the network configuration manually.
While the installer is running you can always switch between the different console screens by hitting Ctrl-Alt-Fn where n is a number from 1 to 9. In the UCS installer, the consoles are used this way:  for the system start messages,   for you to do something,  for a scrolling log of what the installer is doing,  for the graphical console.
So you could switch to console #2, press [Enter] to activate it. The system to be installed is mounted at /target, and therein you'll find log files in var/log. Mostly interesting while the Univention Installer is running are the logs in the 'univention' subdirectory. To watch the join process you would watch the 'join.log' file:
~ # cd /target/var/log/univention
/target/var/log/univention # tail -f join.log
To page through the whole join.log file you would enter
/target/var/log/univention # more join.log
page forward with the space bar, or press the 'q' key to quit the viewer.
Hope that helps as a starting point.