the wire could go from the router to "network in".. and then another wire from "network out" to your computer, that would work
the coax cable could go from the wall to the coax port on the battery backup, and then another coax cable from the cable modem to the 2nd coax port on the battery backup
obviously the computer's electrical wire would go into the battery backup plug (identified as battery backup not just surge-only)
the special wire that came with it, that has an rj45 connector on one end, and usb on the other, would go from the "data" port on the battery backup to any usb port on your computer