Berman was born in Chicago, Illinois, and grew up in Brooklyn, New York. Her father, David Bernstein, was a physician and her mother, Dorothy Bernstein (née Skupsky), managed her father's office practice. Inspired by her hard-working and scholarly father, she was interested in science as a young girl and planned to become a scientist or doctor. Her mother, who was strongly involved in the community and volunteer work, influenced her to be involved in community activities throughout her life.
During high school, Berman worked in Ingrith Deyrup's laboratory at Barnard College. Deyrup encouraged Berman to attend Barnard as an undergraduate. While at college, she worked in a Columbia University College of Physicians and Surgeons laboratory with Barbara Low. There, Berman learned about crystallography, which would become a lifelong passion. She graduated from Barnard with an A.B. in chemistry in 1964.
Following college, Berman attended the University of Pittsburgh for graduate school, a place she selected because it was the only place in the country with a crystallography department, and one of the few where crystallography was offered as a subject. There she worked with George A. Jeffrey on carbohydrate structure, receiving her Ph.D. in 1967. Berman remained at the University of Pittsburgh for two more years as a postdoctoral research fellow.