Yvonne Connolly was born to Irene and Elvert Connolly in 1936.
Martin received a bachelor's degree in 1958 from Carleton College, Northfield, Minnesota. She was the only woman to be a chemistry/zoology major in her year. From 1958 to 1960 she worked as a pharmacology assistant at Abbott Labs. She was awarded a predoctoral fellowship from the National Science Foundation for the years 1960–1963, attending Northwestern University, Evanston, Illinois. She received her Ph.D. in physical biochemistry from Northwestern University in 1964.