The usefulness of the U.S. census took a big leap forward in 1850 with the inclusion of all members of the household. The addition of relationship to head of household, added in 1880, was another big addition. While 1850, 1860, and 1870 lack that relationship information, there is a search strategy on FamilySearch.org that deals with it for years 1850 and 1870.
FamilySearch.org has added a field called “Any Household Member.”
Suppose you are looking for Louisa Raymond. You don’t know where she might be in 1850 and searching on her name returns 250 results. You could check them all, but there is a faster way. Let’s say you know she is working for a Whipple family as a nanny. Enter Whipple as Other Person’s Last Names and Louisa jumps nicely to the top of the search results!
The same capability is available for the 1870 census.
(Unfortunately, this is not possible with the 1860 census. FamilySearch’s 1860 census is substandard. People are not organized into families or households. FamilySearch lists each person in the census separately and alone. It is not possible to see who lives together in families unless you have a Fold3 subscription with which you can look at the images.)
Another good thing to know about all searches on FamilySearch is that locations need to be specified from the lowest level up to the U.S. state or country level. For example, specifying "Smithfield" as the residence place in the 1930 U.S. census returns no results. But specifying "Smithfield, Cache, Utah" returns the expected results.