For the domain name you need to point it to the ip address of your server. This is how domains, and the DNS system, work. They point an easy to remember domain name to a hard to remember IP address.
If you have a firewall running on your computer you need to allow it to access the internet.
If you are using a router you need to open a port (usually port 80) to allow connections to the server from the internet. You also need to set up a static IP address for the connection between your computer and the router, so that it always knows the IP address of the server. This is different from the public IP address you mentioned, this is your private IP address.
The web server may not need the IP address itself, but I haven't used Windows Server before. In some other web server software all you need to set are the port it should listen on (usually port 80), and the domain names it should answer for. That way when requests come in on port 80 it can see if the domain being requested matches the domain you have set up, and if so it looks for the file.
Here's a link to a tutorial on how to add the domain to Windows Server: http://www.addictivetips.com/windows-tips/how-to-create-a-domain-in-windows-server-2008/
You can get your private IP address on a Windows machine by clicking Start > Run > type "cmd" and press enter > type "ipconfig /all" and press enter. In the list of info that is shown it should say "IP Address"