The 1870 federal censu began on June 1, 1870.
The 1870 federal census includes the following information:
-head of household is listed first
-all others in the household are listed next
-personal information for each person including sex, color, age, marital status, ability to read and write, birthplace, birthplace of parents
-trade or profession and number of months unemployed
-whether an individual was blind, deaf, dumb, idiotic, insane, pauper, or convict
Here's a link for an image of an 1870 census page: