I'm always curious when people tell me that nothing interesting has ever happened in their family history or that they know what nationality they are. Most likely they have no clue! I never thought when I started this trip that I would find Presidents, Civil and Revolutionary War soldiers, relatives who fought agains Indian attack and never a tree that I could date back in this country to the early 1600s.
People who are starting out in genealogy will ask me where I get my information so here it goes:
Libraries - obituaries, reference books, local history books
Archives - Reference books, manuscripts, family histories, wills, estate papers, orphan's court
papers, marriage, birth and death certificates, property deeds
NARA (National Archives DC) - Civil War and Revolutionary War Pension records, immigrant
ships's records, other military records, reference books from all states, and more.
Online - http://www.rootsweb.ancestry.com/ (message boards and family trees)
http://www.google.com/ (web, newspaper, and books)
http://www.familysearch.org/ and http://www.labs.familysearch.org/
Heritagequest - You need a subscription for this site. You can usually get one free
with a library card, if your local or county library subscribes. Great for census records,
book resources, magazine articles, revolutionary war pensions and other sources.
Check Historical Societies and Local and State Archives websites, some have great resources on the web
Library of Congress -searchable database and go there (you'll need a library card)
ARIAS - Pennsylvania in the Civil War muster roll and more.
http://www.ancestry.com/ pay service, but free at my local library
NY Times and Washington Post have a searchable database. You may be able to view
some articles in full, others you will have to find at a local library.
DAR museum in Washington DC - great resource for family history books (I'm even in one!)
Historical societies will charge for you to do research on a daily basis unless you have a membership, archives do not charge.
I always try to do as much free research as I can and then hit the pay facilities.
Don't forget to check for obituaries at a library that has the microfilm. Always call first to make sure their microfilm machines are working.
Your local LDS (Latter-Day Saints, Mormon churh research facility) has a wealth of information on microfilm as well. Check their website http://www.familysearch.org/eng/default.asp for locations and available resources.
This list is not complete by any means, just a starting point.