From Plaza de Cibeles, you can follow 6 different self-guided pathways.
Metro: Banco de España (line 2).
There is also a site that gives advice regarding some other walking tours:
www.frommers.com/destinations/madrid/0056010008.html
There are also guided tours; find more cheching:
www.esmadrid.com/es/portal.do?TR=C&IDR=473&IDM=71&NM=3 (different languages)

