If I want to set my Slackware machine to have a static IP assigned from the router, how can I do so?
I assume I have to disable DHCP then edit something to set the requested IP, but I'm not sure where.
(I don't have a GUI)
This heavily depends on whether or not your router supports it.
You do not need to disable DHCP, the DHCP reservations will need to be provided by your router and the router should have to set up a static standing reservation of the MAC address of the network interface to an IP address.
Of course you don't have to and you can disable DHCP and set up a static IP address altogether on the system by editing