If the residents (or owners) of a property were well known, they may appear in biographical sources, historical newspapers and other periodicals, digital collections of directories and photographs and other images. Otherwise, you can go searching for information about people in records used by genealogists: censuses, passenger lists, property deeds, probate records, city directories, vital records, local newspapers, published family and local histories.
See Genealogy: Getting started in Genealogy for an introduction to some of the resources listed above.
Searching New York State and United States Federal Censuses by address will reveal the occupants of a (residential) building at the time the census was conducted. To do this, however, you will need to discover what Enumeration District the building was in at the time the census was conducted — this is known as the ED number, and is not the same from census to census. You can do this by referring to an ED number generator, available at a site called One-Step, or by consulting election maps and indexes, in print or on microfilm, in NYPL's Milstein Division. Censuses are available free at FamilySearch, and through subscription genealogy databases like Ancestry Library Edition.
The 1950 U.S. Census and census maps (see below) are available from the National Archives.
For more information, please consult Searching the Census by Address
Below: U.S. Federal Census, 1900, NY, NY, Manhattan, ED 100, 10B: Carsten Gerken, the first owner resident of the 135 Waverly Place / 77 Sixth Avenue, aka The Waverly Diner, 385 Avenue of the Americas.
Obituaries, biographical details, and stories pertaining to a building's owners and occupants (and for that matter the building itself) may be found in old newspapers. The New York Public Library provides free at the point of service access to numerous historical newspaper databases, including
Many newspapers are often not digitized, and may be found on microfilm or microfiche in The New York Public Library Microforms Reading Room.
Above: New York Herald, June 22nd, 1894, p.1 (ProQuest Historical Newspapers)
City directories - available through NYPL Digital Collections, subscription databases like Ancestry and Fold3, and on microfilm here at the library - will generally list the head of household, their occupation, and home and business addresses. They were published annually in New York City from 1786 until 1933/34. Read more about city directories here.
NYC city directories 1849-1922 are currently available to download as pdfs or txt files (meaning that you can Ctrl-F search for names and address (Command-F in a Mac). Bear in mind, you are searching pixels, and city directories use abbreviations. E.g. 135 Waverly Pl. Or 16 E. 14th [Street].
Telephone directories began in the late 19th century and are also available on microfilm at NYPL, as are telephone address directories starting in 1929. Address directories, as the name suggests, are searchable by address and will list the subscriber's name, but not all other household members.
Address directories can be used to search by an address, rather than by name. Some address directories include name and address lookups.
For more information about accessing city directories, and telephone directories, please see Genealogy : Getting Started at The New York Public Library: City directories.