Having recently implemented SAML authentication for an application I found the most useful information in the OASIS SAML2 technical overview document. It's very readable and contains real examples of the XML messages that are passed.
Section 5.1 describes the interaction of having YOUR application (service provider or SP) request authentication to a remote identity provider (Idp).
http://wiki.oasis-open.org/security/Saml2TechOverview