Garner was born in Houston, Texas. Her mother, Patricia Ann (née English), was an English teacher from Oklahoma, and her father, William John "Bill" Garner, worked as a chemical engineer. When she was four years old, her father's job with Union Carbide relocated her family to Princeton, West Virginia, and then later to Charleston, West Virginia, where Garner resided until her college years. She has credited her older sister, Melissa Lynn Garner Wylie, who resides in Boston, Massachusetts, as a source of inspiration to her. Her younger sister is Susannah Kay Garner Carpenter.
Garner's conservative upbringing included going to church every Sunday, not wearing make-up or a bikini, and waiting at least until the age of 16 to be allowed to get her ears pierced, which, she later joked, made her family "just a step away from being Amish". She said: "I'd hate to say it was strict. It was just not condoned. I never felt hemmed in." She began taking ballet lessons at the age of three and continued to dance throughout her youth, but she did not envision herself becoming a classical ballerina.