KBlackBox is a KDE application. Therefore you need to have KDE installed on your computer - at least kdesupport, kdelibs and kdebase packages. The actual installation is very easy:
cd somewhere
gunzip kblackbox-x.y.z.tgz
tar -xvf kblackbox-x.y.z.tar
cd kblackbox-x.y.z
# This is for generating the configure script. It will be probably removed,
# when kblackbox is a part of kdegames.
make -f Makefile.dist
#
./configure
make
make install