Step By Step Research 

For relatives that died after 1950, search the Social Security Death Index (also at Steve Morse's Searching SSDI in One Step).  The index will provide an individual's date of birth, date of death, place of death, and their social security number.  With this information, you can send away for a copy of the individual's Social Security Application that was filled out and contains information on the individual's place of birth, home address, and names of both parents.

Search for a Death Certificate. Death certificates will usually provide date of birth or age at death, date and place of death, medical reason for death, funeral home, burial location, and parents names and their location of birth. For deaths in New York City prior to 1948, search Italiangen's NYC Death Index to obtain a date of death, county where death occurred, and a death certificate number.  Contact the Vital Records Department in the state that death occurred to obtain a death certificate.  Certain limitations exist as to the length of time since death that these records are kept private and vary from state to state.  Death Certificates were also filmed by the Family History Library and these microfilms can be ordered by FHL centers and certain libraries.   Copies of records can also be ordered directly from FHL by filling out a Request for Photocopies form with the necessary information.  In either case, you will need to know the microfilm number.  Using Steve Morse's Searching the NY Death Index in One Step will provide the microfilm number for deaths in NY boroughs between 1862 and 1948.

Search for an Obituary. An obituary will usually provide names of living relatives, funeral home and possibly a burial location. Use various online newspaper resources to find an obituary.  For example, the New York Times, Ancestry.com, AncestorHunt  ...  Alternatively, you can contact a librarian at the local library of the location of death and provide a date of death in order to search a local newspaper.

Obtain a picture of the tombstone which may provide a father's name. First see if the cemetery has information online and a service to take pictures of the tombstone. Search the JewishGen Online Burial Registry, Jewishdata.com (fee for image), and Find A Grave.  Local genealogical societies may have tombstone photography projects so check those online.  You can ask someone to take a picture by emailing the Jewishgen listserve or using Random Acts of Genealogical Kindness.