How to change SQL Server in a domain with a new server machine and latest SQL database? We have an SQL Server in our domain.
The SQL Server version is MS SQL 2000 and the Operating System is Windows Server 2003.

Now I want to change the machine itself with new computer running windows server 2012 and SQL Server 2008. 

How to do this ?
What you are planning is called side-by-side upgrade. It means that wholly new system is installed. Its alternative is in-place upgrade. It means that only the Sql Server is upgraded on existing computer. As you are going to upgrade the operating system too, side-by-side is the only option.

Microsoft has released a white paper about how to upgrade Sql Server. The pdf has 400+ pages, but not all parts are likely to be relevant to your case.

Read the documentation and ask for clarifications about things you didn't quite catch.

As a side note: though migrating from Sql Server 2000 to 2008 is certainly an improvement, you really should migrate to more recent version. That is, Sql Server 2014 or 2016 should be your migration target. Be aware that Sql Server 2000 is so old that it cannot be migrated directly to Sql Server 2012. An intermediate step into Sql Server 2008 is needed.