Once you've setup the Slingbox for viewing locally, its the routers responsibility to allow remote viewing. You'll need to make sure that that the corresponding public UDP and TCP ports and being forwarded to your Slingbox's private IP address. Here is Verizon's helpsite for port forwarding (http://www22.verizon.com/ResidentialHelp/HighSpeed/Networking/Troubleshooting/PortForwarding/123866.htm)
Other reference articles to get the information that you might need.
IP address and Port Number: http://support.slingbox.com/get/KB-005866.html
Port Forwarding: http://support.slingbox.com/get/KB-2000068.html
Network Setup Assistant: http://support.slingbox.com/get/network-assistant.html
Manual Changes: http://support.slingbox.com/get/KB-5000126.html