Are you asking how you can find the public IP of your router? From any computer inside your network go to http://www.whatismyip.com and it will tell you.
If you want to access your Arduino from the Internet then in your router you would add a rule to forward TCP port 80 traffic from the public interface to the IP address of your Arduino. Different routers do this different ways; if you can't figure it out let us know the model # of your router and we'll try to help.