Step by Step instructions on how to complete a SharePoint Server (SPS) 2003 migration to SharePoint Server (MOSS) 2007 can be found at the following links.
Scenario: To migrate a SPS 2003 portal that consists of three SQL Server databases: Outofthe1_SITE, Outofthe1_PROF and Outofthe1_SERV. The Outofthe1_SITE database contains the site collections for both the portal and all the My Site site collections. SharePoint Server 2007 is already installed on a machine and basic services configured. The new portal will have a URL of http://obe once it is migrated.
The content database migration consists of the following steps: