I have a similar system set up here at my home and work - so here's how you need to set it up:
Hardware: One non-wifi router with 4, 8, 16 or 32 ports, whatever you need. One WIFI router with 4, 8, 16, or 32 ports, whatever you need. 100 feet of ethernet Cat5e cable with RJ45 ends, one 6 ft or so cable with RJ45 ends to plug the last computer in.
Layout:
Wired router will have a WAN port, and the rest will be LAN ports. Assuming you're connecting all this to the internet, you'll use a short network cable to connect the WAN port to the cable modem (or appropriate network interface).
100 foot cable will be plugged into one of the LAN ports, and will go to the WIFI router and be plugged into one of the LAN ports (NOT the WAN...