Born in Los Angeles, Armer received a bachelor's degree in speech and drama from Stanford University, a master's degree in theatre arts from UCLA and an honorary doctoral degree from California State University, Northridge.
After college, Armer started his entertainment career at a radio station in San Jose where he worked as an announcer. After moving back to Los Angeles in search of a radio job, Armer began working at an advertising agency that specialized in television ads. In that role, Armer later wrote, acted in, directed, narrated and edited television commercials. From there, Armer and a relative by marriage Walter Grauman developed their own television show, Lights, Camera, Action, which aired on NBC affiliate KNBH for three years. He later was hired by the station as a floor manager and then director. He later went on to 20th Century Fox, where he wrote, produced and directed several television series, including My Friend Flicka and Broken Arrow.
Armer later became executive producer for The Untouchables. He joined QM Productions where he produced The Fugitive for which he received the Television Academy's Emmy Award, The Invaders, and the first year of Cannon. For his work on The Fugitive, Armer won a 1965 Edgar Award from the Mystery Writers of America, a "Most Popular Series" award from TV Guide Magazine and a Producers Guild Award. He later became a member of the Producers Guild's Television Hall of Fame. In 1980, he became a part-time faculty member at California State University, Northridge, and eventually became a full professor and head of the Screenwriting Option, of the Cinema and Television Arts Department. Armer taught directing, as well as all levels of screenwriting.