Two ways to do this:
1. If your IIS machine has a real IP. If this is the case, you need the dns to point to the machine directly (see Boner's post). So for this, you need a record like:
www.1234.com A 123.123.123.123
which points the requeting web browser to your machine, if the 123.123.123.123 is the IP address of your machine.
2. If your using NAT/DHCP. In this case, the server's IP address is a fake, and requests have to be forwarded through the router. So here, you setup the DNS record to point to the OUTSIDE address on the router (the one the ISP gave you). So, you do that, then you setup the router to allow the port through, and (if it's a linksys, or somethig like that), you setup port forwarding, which says requests on a port (port 80 for web requests), get forwarded to the internal IP address.
Based on what you've described, you probably have the second item here, so you should check your router instructions on port forwarding & triggering. Post up some more info (like your router type, the ip on your machine) and this'll be easier to figure out.