Right now , I'm downloading the tgz-files for KDE 3.1.4 and before attempting to install it , I'd like to know the following:

Is there an easy way to install all the files at once (by means of a script , perhaps)

If this is not the case and I have to do the tar -zxvf-etcetera-dance for each file : In what order do they need to be installed?
I figure "KDE-base" should be first , but from there?

There isn't any script floating around that I know of however it is still fairly easy. You actually need to compile the arts package first, then kdelibs and then kdebase. After that it is your choice what order you do the rest in as all the rest are optional (but nice). If any of these packages give trouble it is not the end of the world (kdebindings once just refused to compile for me so I left it).

P.S. KDE will probably require quite a new version of Qt. It will tell you if your version is too old. Fortunately Qt is quite easy to compile.

Uhm....
How do I check the version of QT?
I think it's a non-issue , given the recentness of my distro's release , but it would be handy to know anyway.

There is an script actually! It's called konstruct. You can download it from the KDE site.