Martin grew up in Timberlake, Virginia, just outside Lynchburg. The women in her family shared the name Carolyn, earning nicknames "Buck" (grandmother), "Boolie" (mother), and "Biddy" for Martin. She graduated from Brookville High School in 1969, where she was valedictorian and set the school scoring record for girls' basketball. She received her undergraduate degree from the College of William and Mary in 1973, where she was a member of Phi Beta Kappa. She earned an M.A. in German Literature from Middlebury College’s program in Mainz, Germany and received her Ph.D. in German Literature in 1985 from the University of Wisconsin–Madison, and joined the faculty at Cornell the same year.