Basically:
If you are trying to connect the laptop to the web through the Slackware box, then on the Slackware box be sure to enable /etc/rc.d/rc.ip_forward. That startup script will do what uppman suggested during every (re)boot. The Slackware box would need an additional network card (one to connect to the router and one to the laptop).
If you are trying to connect the laptop directly through the router, then configure the laptop to look for a gateway at the router's local ip address. The router should be configured to provide network address translation. In Slackware the gateway is configured in the /etc/rc.d/rc.inet1.conf file. I don't where this is done in BSD.
This presumes the router is actually a router and not a switch.