The U.S. Census Bureau has a 2010 Census Home Page with links to additional resources:
Population profile maps
Quick population finders
Census Bureau special reports and briefs.
If you're unfamiliar with the purpose of a census and how it's carried out, a good starting place is What is the Census?
Beginning with the 2010 Census, only one census form was distributed to U.S. households, the Short Form, which asked only 10 questions from the following categories:
Additional demographic information formerly collected through the Census long form, such as income, educational attainment, marital status, etc. is now gathered by the American Community Survey (ACS), a multi-year sampling program.
ACS demographics are not included in 2010 Census tables, although ACS data is in American FactFinder. For example: if you search for a 2010 Census file containing income data, you will get no results because income data was only gathered in the ACS.