There are two ways to go about doing this. The first and the easy way is to use the dedicated router with the server and one NIC. Set the router up to accept the DHCP assigned IP address from your ISP. On the router turn off the DHCP function. For the one NIC on the server use static IP addressing in the same IP range as the router. I usually reserve the first 20 or so IP's for static applied addresses for servers, printers ect. DNS should match the server address and the default gateway should be the address of the router. So for instance if you are using a standard linksys router which defaults to 192.168.1.1 the server should be assigned an address from 192.168.1.2 to 192.168.1.20. The subnet mask stays at 255.255.255.0, the default gateway would e 192.168.1.1 and the DNS would the SAME IP as the one you assigneed the server. DHCP would then be set up on the server with an IP pool based off of 192.168.1.0 you will exclude the addesses 192.168.1.1-192.168.1.20 for your staic addresses so you don't end up with conflicts later. The DNS IP will be the same as the server and the default gateway will be the address of the router. This setup will allow internet access as well as allow DNS resoultion for your domain if you set one up.
Way two uses the server as the router, which by the way Microsoft recommends against doing since the server is then exposed to the internet, and two NIC's. NIC 1 will be set up the same as the NIC in the scenario above with a static IP with the exception of the default gateway. DHCP will be set up the same as well. The second NIC will use DHCP and will be connected directly to the modem. The next step will be to set up Routing and Remote Access on the server. It is installed by default but not activated. Go to the snap-in to activate it. Choose the default action for VPN or NAT setup and follow the wizard. Check this link HERE
. It is possible that NAT will not allow you to use DHCP for your internet connection. IF this is the case you can use the your router instead connecting it the the internet side of the server only. Then you can apply a static address on the internet side of the server that matches the ip range of the router.
Get your facts first, then you can distort them as you please.