Shane, Mac has Satellite and DSL, so it is going to be a little "trickier" than initially thought. Wouldn't you think he could call his provider and them to issue him a new IP and tell them he believes someone is watching his current IP. I would think that would be enough to get them to comply.
To change it you just need to log into the router and change it MAC address then reboot the cable modem. The modem will see a new MAC and give it a new IP.
Don't some ISPs look for the MAC address of the modem itself. I know with mine if I use a different modem then I have to contact them and give them the new MAC...they don't care about the router though.
Mac, like Shane said, the router takes the Internet IP and basically creates it's own little internet for your home. The "192.168.10.1" is that new "local" internet that's just for you. That number can only be seen and used from inside your network, which is why it's okay to post in the forum. You Internet IP is the same as your home address. If people know that then they know exactly where you're located.
But like I said before Mac, do you know if you need to change your Internet IP? You might have a different issue. Do you just want your Internet IP to be different so that you can't be "seen"?
-Evan