To build Kile, you will need a Latex distribution like TeTeX or
Tex-Live. Slackware 13.0 (and lower) include the former distribution
and it is available on the installation disk(s) if you did not do a
full install.

WARNING: This version of Kile is a Beta release, since it is still being
ported to KDE 4, so make sure you hit the "Save" button every now and 
then ;)