When I try to copy or move my files in Konqueror (which I prefer to Dolphin as my file manager), the dialog box with progress bar and details of the files being copied doesn't show up. My distribution is Gentoo Linux. I emerged just kdelibs, konqueror and dolphin parts, because I don't use the whole KDE, just its file manager and a couple of other programs from KDE. My default desktop environment is XFCE.

Did I miss some package maybe?
Or the progress dialog is turned off by default and I need to turn it on manually somehow?
What do I need to do to get the usual progress dialog box back?
Without the progress bar, I have no way of telling whether the copying process succeeded or not, and whether all the files has been copied or just a few of them.

Please right click on the Notifications applet > Notification Settings, and make sure "File transfers and other jobs" is unchecked if you want to use a normal, dialog based progress notification.

After doing this you will need to logout and back in again for it to take effect.

Could it be done by editing some config file instead?
As I've said, I don't have full KDE environment installed, just selected apps, so I don't have "Notifications applet" or anything as such, because I don't use KDE desktop nor panel. I use XFCE 4. And KDE doesn't seem to display any notifications there in the XFCE notification area when I try copying files.

Is the command "kuiserver" available?

Nope, it isn't.
I can install this package perhaps, if there isn't any other way to do it.
But I would rather like to avoid installing unnecessary software just to change one option.

The kuiserver daemon is required for KDE applications to be able to show progress dialogs. Because file transfers can continue after an application has finished (due to how KIO works) an independent process is needed to display the progress.

OK I installed kuiserver and the dialog box is back.
Thanks for your helpful and informative answers

No problem. Please file a bug report with your distribution as kuiserver is a mandatory component which should always be installed.