Once you've setup the Slingbox for local viewing, the only step left is to confgure port forwarding for remote viewing. Port Forwarding is a way to allow public internet access of a particular to be directed to a specific device in your network.
Here's a website that has instructions for many routers, take a look at it. Hopefully you'll find yours listed. (http://portforward.com/english/routers/port_forwarding/Apple/AirPortExtreme/SlingBox.htm)