KDE-Forum.org

You can use Konstruct to download all the sources and compile it. I don't know how to use it exactly: I never used it.

You can also compile it file for file. You then unpack the source, execute ./configure with the arguments you need (such as --prefix=/place/to/install). If you need a package, configure will tell you. After that, you can run make and su -c "make install" to install it. You then have to do that for all modules, beginning with arts and kdelibs (the rest of the sequence doesn't matter).

I think that in most cases "Konstruct" is easier.

Hello

You can find Slackware packages for KDE 3.4 from linuxpackages.

I have used Konstruckt to compile KDE, but I have never used it for a system wide installation, still I would imagine that system wide installation is quite easy.
When I compile software for Slackware I use checkinstall, which can found under extra directory in Slackwares ftp servers. Checkinstall makes Slackware packages so I can easily track and uninstall software that I have installed on my system.

All and all, installing KDE from sources to Slackware is pretty straight forward thing to do, there are few libraries that you might also have to install from source or you could look if they can be found from linuxpackages.

Good luck!

ps. good instructions for installing KDE from source can be found from here