For New York passenger arrivals after 1910, the Soundex (index) cards on microfilm will give you something that looks like this...|
DOE, John 32m 2 10 3904
The information given on these cards is arranged like this...
name, age (& sex), line number, page number, volume number
So the above soundex card says that John Doe, a 32 year old male can be found on New York passenger record Volume 3904, page 10, line 2
You then go here and look for the corresponding volume number...
NARA Microfilm Numbers for New York Passenger Lists
to get the NARA (National Archives) microfilm roll number for that volume number -- in the above example John Doe would be found on Roll #1765 which covers volumes 3904--3905 for the date Oct. 31, 1911
These New York passenger records are part of this series of microflim: Passenger and Crew Lists of Vessels Arriving at New York, NY, 1897--1957; T715 (8,892 total rolls) -- so John Doe's microfilm is Roll #1765 of NARA series T715, which can be abbreviated as T715-1765.
If you need FHL (Family History Library/LDS) microfilm numbers for rolls that can be ordered from any Family History Center then choose one of these weblinks for the time frame you need...
NY Passenger Records with FHL Roll Numbers 1910-1919 Volumes 3071-6332
NY Passenger Records with FHL Roll Numbers 1920-1929 Volumes 6333-10142
NY Passenger Records with FHL Roll Numbers 1930-1942 Volumes 10144-14316
note: Vol. 10143 is on FHL Roll #1756392 (this roll is not listed at the link above, but it is available from the FHL)
Again you match up the volume number to get the appropriate roll -- John Doe's list can be found on FHL Roll #1400449, which covers v. 3904-3905 for Oct 31, 1911.
After you obtain the microfilm use the page and line numbers to find your passenger -- note that most rolls have more than one volume so you'll have to find your specific volume on the roll first, then use the page and line numbers. Also be aware that each page of each passenger list will have two page numbers, one that is for the individual list, and one for the volume that list is included in -- the page number given on the soundex card is for the volume page number, not the individual passenger list page number.