Actually, to migrate from Windows Server 2003 domain to Windows Server 2008 domain, there are two options:
1.ADMT if the customer would like to create a new domain and new forest.
2.Upgrade if the customer would like to keep the current domain structure;
Option #1: Use ADMT to migrate to a new forest
This involves moving all your resources from Windows Server 2003 domain to a new and fresh Windows Server 2008 domain. There is a tools called Active Directory Migration Tool (ADMT) which is designed for this job.
As far as I know, ADMT v3.1 is designed for Windows Server 2008 AD migration. (Windows server 2008 R2, Not support)
For your information, please refer to:
To download the ADMT v3.1, please visit the below link:
Step by Step ADMT v3.1 Guide, you can refer to:
Option #2: Upgrade the existing Windows 2003 AD domain to Windows Server 2008
If you want to upgrade your original Window 2003 AD to Windows 2008 AD, you can refer to this TechNet online article: