The detail you want won't fit in this small space so I'll write in high level that your average IT or user uses.

There are choices your server admin needs to make to either give the server internet access and then use ICS (Microsoft's feature), SQUID or other to share the internet or just let the router do the DHCP and set the server at a known IP outside the DHCP scope.

Your server administrator picks the plan and implements it. If they are not up to speed, then call in how admins your server for a chat.