The DG Justice website is a good starting point with its guide to the so-called Citizenship Directive (38/2004) which concerns free movement of EU citizens and their family members.
The EUR-Lex website has a more detailed analysis of the Treaty articles and legal framework.
The case law of the Court of Justice of the European Union (CJEU) has given substance to EU citizenship, making it the fundamental status of nationals of Member States.
DG Employment, Social Affairs and Inclusion has extensive information and guides on the coordination of social security arrangements (Regulations 883/2004 and 987/2009), including an FAQ, and is a good source for studies and statistics on labour mobility. This DG also supports an observatory on free movement of workers.
Yet another department, DG Growth, deals with the recognition of professional qualifications (Directive 2005/36/EC).
The information scattered across Commission Departments is brought together on the Your Europe website.