How did Norma Klein die? There is no information about this on the internet.
First, a Google search on the name "Norma Klein" pulls up several references to her life and death, including the New York Times obituary (link below), which appears in the first page of results. Thus there is information about this on the internet.
Norma Klein, born on May 13, 1938, was a popular young adult novelist who died at the age of 50 on 25 April 1989 in St. Luke's Hospital in Manhattan after a brief illness. Her works were especially known for tackling unsettling or controversial topics and several had been banned from libraries.
For an extended biography of her, you might consult the book Presenting Norma Klein (Twayne US Authors) by Allene Stuart Phy.