I'm assuming you have DSL (high speed Internet through a phone line that doesn't interfere with phone calls).
With one computer, the order is
Computer ----- Ethernet cable -------- modem --------- telephone cable -------- wall jack.
With a router, it is:
Computer A ------- Ethernet cable --------- router LAN port (numbered 1, 2, 3, or 4)
Computer B ------- Ethernet cable --------- router LAN port (numbered 1, 2, 3, or 4)
Router WAN/Internet port -------- another Ethernet cable --------- DSL modem ---------- telephone cable --------- wall jack.