First thing to do is physically run the ethernet wiring from the ONT to the router. You will then have to call Verizon to change your connection to ethernet from MoCA. You can also try VZ Direct at dslreports.com to help you.
Second you will have to connect your router in place the Verizon router. You will then connect the ethernet to the WAN port of your router. The TV will will connect to the LAN port.