Enumerators of the 1860 census were instructed to record the names of every person in the household. Added to this, enumerators were presented with printed instructions, which account for the greater degree of accuracy compared with earlier censuses. Enumerators were asked to include the following categories in the census: name; age as of the census day; sex; color; birthplace; occupation of persons over age fifteen; value of real estate; whether married within the previous year; whether deaf, dumb, blind, insane, a pauper, or a convict; whether able to read or speak English; and whether the person attended school within the previous year. No relationships were shown between members of a household. The categories allowed Congress to determine persons residing in the United States for collection of taxes and the appropriation of seats in the House of Representatives.
The following states and territories were enumerated: Alabama, Arkansas, California, Connecticut, Dakota Territory, Delaware, District of Columbia, Florida, Georgia, Illinois, Indiana, Iowa, Kansas Territory (includes parts of Colorado), Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Nebraska Territory (includes parts of North and South Dakota, Montana, and Wyoming), New Hampshire, New Jersey, New Mexico Territory (includes Arizona), New York, North Carolina, Ohio, Oregon, Pennsylvania, Rhode Island, South Carolina, Tennessee, Texas, Utah, Vermont, Virginia, Washington Territory and Wisconsin.
The official enumeration day of the 1860 census was 1 June 1860. All questions asked were supposed to refer to that date. By 1860, there were a total of thirty-three states in the Union, with Minnesota and Oregon being the latest editions.
There were no substantial state- or district-wide losses.
Taken from Szucs, Loretto Dennis, "Research in Census Records." In The Source: A Guidebook of American Genealogy, ed. Loretto Dennis Szucs and Sandra Hargreaves Luebking (Salt Lake City: Ancestry, 1997).
FamilySearch has added a nearly complete index of the 1860 census to its  website, and it has sophisticated display and filtering mechanisms. The index links to images provided by Fold3.com, which is a pay service.
HeritageQuest provides access to the 1860 census that many people can access for free through their local library. Their interface is very straightforward, but somewhat difficult at times because no effort is made to expand searching beyond the exact letters you type -- there is no soundex search, no spelling correction, and no smart name checking (Robert doesn't return Bob or Robbert). Check your local library's website for more information.
Paid access is also available through Ancestry.com.
If you wish to display a table showing a family as they are shown on census returns, use Template:1860-UScensusData. This template does not generate a source citation, which must be entered separately.