The Cold War actually influenced this. The 1950s The Minimum Muscular Fitness Tests in Children was used to assess the fitness of school children in the United States. More than half failed, which led to concern that American youth was weak. In response, President Eisenhower and his advisors established the President's Council on Youth Fitness and the President's Citizens Advisory Committee on the Fitness of American Youth. The AMA and AHA also got involved. This continued into the Kennedy administration--JFK even wrote a piece for Sports Illustrated called "The Soft American."

Regarding specific fitness techniques: resistance exercises were popular thanks to Jack LaLanne, who promoted pulley machines and leg extension equipment. In the 50s, he launched a TV fitness program, which was, at that time, a rarity. In terms of cardiovascular exercise, it was highly influenced by military exercises such as running and jumping jacks. Vibrating machines like this one were promoted as a way to "break up fat" (obviously that was fake)

Regarding diet, there were lots of ideas. People bought weight loss soap (?!) as well as diuretics and laxatives to help purge extra weight. Portions were smaller then, which is important to note. Diets for weight loss usually allowed for carbs and were lower in fat. There were fads like the "10 Day Miracle Diet." I think it is also important to note that, during this time, more women used amphetamines to use weight because they were easily obtained from doctors.