Getting online. Issue "netconfig" as root. That's the same app Slackware used on the install. Then you just need too know things. This is also in
Slackware Linux Basics: For Slackware Linux 10.2 so I won't bother typing it out for you. Just go through the steps there -- Daniël even put screenshots -- and write down what you need. Then when you do it in Slack, you'll be ready.
Your monitor is easily overcome, but right now I'm drawing a blank and otherwise occupied. Search LQ and the answer is here.