Install apache and php (if you haven't allready).
Configure apache in /etc/apache/httpd.conf ,and enable the php module in that same config file.
If you're box is direct connected to the internet configure IPtables. (secure your box)
If it is behind a router don't forget to forward packets on port 80 to your slackware server
If you want your website to be reachable on for example
www.nukey.nl register a domain and forward DNS to your own IP.
There are also a few free websites that offer services to map a domain-name to your IP (dyndns.org for example ), but it's always nicer to have a real domain to own. Costs me 12 Euro a year.
What do you mean by DNS Server tool, you won't need that if you're just running a webserver.