The official U.S. Census is described in Article I, Section 2 of the Constitution of the United States. It calls for an actual enumeration of the people every ten years, to be used for apportionment of seats in the House of Representatives among the states. The first official Census was conducted in 1790. That census, taken by U.S. marshals on horseback, recorded information on 3.9 million inhabitants. Since that time, the Census has been conducted every ten years, generally on April 1 in years ending in a zero.
The original census ledgers showed, household by household, each person living in the U.S. Earliest census records varied in the amount of information provided for each household. Starting in 1850, it began listing characteristics of all individuals in a household and usually included their name, age, sex, place of birth, income level, ethnicity, occupation, and education. Because the Census contains personal information, by law, it cannot be released until the information is 72 years old (roughly the life expectancy in the USA, or at least it used to be). All individual census records in the USA are open to the public up through the 1940 Census. The 1950 Census will be released in 2022, the 1960 Census will be released in 2032, etc.
Immediately after each census is taken, the U.S. Census Bureau tabulates all the raw data, removes any personally identifying information and publishes summary reports - e.g., the number of teachers in each county/city/state, the number of individuals in each age group, average number of children in each family, average income levels in a specific geographic area, etc.
For a list of questions asked in each census year, consult the Census Bureau's Index of Questions or Measuring America. Searching for specific types of statistical data within the census can be tricky. The Census website has quick links or you can search using the American FactFinder interface.
The Census Bureau also publishes an Economic Census and the Census of Agriculture (which has moved to the USDA website) every 5 years. In 2005, the socio-economic information collected on the Census Long Form was moved to a new product called the American Community Survey. In addition, there are a number of specialized censuses - see the Specialized Subjects tab for more details.