Today the National Archives has released the complete digitized records for the 1940 census. These records are the actual questionnaires, with the answers provided by households, used in the 1940 Census of Population and Housing. By law these records are kept confidential for a period of 72 years. If you are interested in looking at how some of your relatives answered census questions in 1940, start with a Research Guide from the Archives, which includes a FAQ, background information, the questions asked in the 1940 census, finding aids, videos, and more.
Of course the data from the 1940 census has been available for decades. Information on census data 1790-2010 can be found using the Libraries’ subject guide, Decennial Census Information at Columbia University Libraries. For more information on actual census records through 1940, use the Ancestry Library database.