Uhmmmm, rpvl's got the right idea.
Why is everyone going outside their router when their collection is inside? All I did was start the calibre server on my laptop (running linux, but that's irrelevant), then go to its ip address:8080. Works perfectly. Ubuntu instructions:
Run calibre, start up the server on a port higher than 1024 (I left it as the default, 8080).
Open a terminal, type in: sudo ufw enable
sudo ufw allow 8080
Right click on the network icon on your panel
On your kindle, type in the ip address of your computer as it's shown on the connection info window, along with the port number.
In my case, this was "http://192.168.1.8:8080".
The instructions are pretty much identical for other linux distros, windows and mac. Just don't forget to open up the correct port using your firewall. You really don't need to use your external ip address or anything like was described in the original post unless you don't have a wifi router or if you want to access your collection away from home.