Okay, then.
First of all, the question that comes to mind is why you want Qt installed. If you want to install a Qt-based program, then installing that in the App Manager will pull all the needed Qt dependencies with it utomatically. If you want to develop Qt-based apps, that's another thing altogether. Apart from that, I don't understand what you'd need them for. The Qt libraries in the link I gave you just provide support for applications that use Qt instead of GTK/Hildon. Installing them by themselves will make no noticeable difference.
As for apt-get on the command line, hopefully you have familiarized yourself with the basic syntax. If not, here's what you need to know:
the file name of the package is in three parts, separated by underscores:
libqt4-core_4.4.1-1maemo2_armel.deb
the first part is what you'd type into the command line with apt-get to install it. The second part is the version, and the last part is the processor architecture (ARM, in this case).
So provided that this file was in a repository that you have set up on the device, you could install it with this command:
apt-get install libqt4-core
and remove it with:
apt-get remove libqt4-core
If you manually downloaded a *.deb file (not recommended unless needed), you can install it with:
dpkg --install /path/to/file/libqt4-core_4.4.1-1maemo2_armel.deb
and remove it by changing --install to --remove
Notice that you need the whole filename with this method. If you did this, it would likely complain at you, and tell you that you need to go download a whole bunch of files and install them first. That's why we have apt-get :P

Hopefully this helps, and I apologize if you already knew some or all of this. If you tell me what you're trying to accomplish, I may be able to help some more.

Cheers,