There are many excellent sites on the Internet offering free genealogical information, education and resources.
A good place to start is Cyndi’s List of Genealogy Sites on the Internet.
Rootsweb is well-known for providing genealogy message boards and mailing lists. You can affiliate by surname, location or interest.
To search for your family in census, birth, marriage, military and other records try Family Search. This site is operated by the Church of the Latter Day Saints (LDS) and its offerings are growing,
A great site for immigrant passenger lists and ships is the Immigrant Ships Transcribers Guild(ISTG).
For old books, local histories, biographies and other compilations try Google Books.
Ancestry.com offers free access to the 1940 Census Records.
History at Home: A Guide to Genealogy is a very nice guide for the beginning genealogist with many links to other great articles and reference works.