You want to determine the IP address for a computer based on its domain name by performing a Domain Name System (DNS) query.
Use the System.Net.Dns class, which wraps this functionality in the GetHostByName method.
On the Web, publicly accessible IP addresses are often mapped to host names that are easier to remember using a network of DNS servers, which are a fundamental part of the Internet backbone. To perform a DNS lookup, the computer might contact its cache or a DNS sever (which might in turn forward the request to a DNS root server).
This entire process is transparent if you use the System.Net.Dns class, which allows you to retrieve the IP address for a host name by calling GetHostByName ...