Here are a few websites I use regularly to conduct my research:
Family Search – this is an amazing site that has access to tons of digitalized records broken down by geographical area. Best part is that it’s FREE!
Ancestry.com – this site is probably the most complete genealogy website, including user-submitted family trees, census information, digital books, military records, and vital records. Subscription-based, but worth it.
Cyndi’s List – a great free indexing source with lots of links to genealogy websites and resources, organized by state (and country).
National Archives – this site particularly has a lot of good U.S. government and military records as well as historical books and magazines.
Daughters of the American Revolution – this site has a good online research tool as well as books and other media to help link your family back to “Patriots” that fought in the Revolutionary War.