Connecting to SQL Server 2008 on windows server 2008
You will be using the servername (DNS) or the IP address of the server.  But if you have a named instance (as opposed to the default instance), your servername will be followed by \instanceName.

So, in other words unless you changed any SQL Server Express install defaults, you should connect to the server like this:

yourServerName\sqlexpress


SQL Server Express has a default named instance name of SQLEXPRESS.  Also, since SQL Server Express is a named instance, you'll need to ensure that your SQL Server Browser service is running.

Another one.  If you are trying to connect to SQL Server from a separate machine, you'll need to ensure that the TCP/IP protocol is enabled for SQL Server.

The above two points can be verified and configured in SQL Server Configuration Manager.