She was born in Boston, Massachusetts, on March 21, 1897 to Walter and Margaret M. C. Foley. From 1909 to 1915 she attended Boston Girls' Latin School, and even then aspired to be a writer. The school magazine published her first short story Jabberwock when she was eleven years old.

Her aspirations were present even before this. When she was seven both her parents fell ill, and were unable to care for her. She dealt with this by writing a novel about a fortunate girl who got to go to boarding school. At about this same time she became an avid reader, escaping into fiction. It is surmised that this laid the foundation for her later literary achievements, and when she developed an astute sympathy for the human condition.

After graduating from the 'Girls School' she attended Boston University but did not graduate.

After leaving Boston University, she chose a career as journalist and foreign correspondent for a succession of newspapers. These included the Boston Herald, the San Francisco Record, and the New York Daily News. In 1925, she met her husband-to-be Whit Burnett in San Francisco. In 1927 she joined him in Paris, where she worked for the Paris Herald and wrote fiction. They were married in Vienna in 1930, and their son David was born the following year. Martha and Whit were passionate for each other and for literature. In 1931 she convinced him that they should launch a magazine for short stories only.

The objective for the new publication was to publish short stories with merit or quality above the commercial mainstream of American magazines. Believing readers and writers were capable of more created this focus. In a short time their magazine "Story" became notable. From the first printing, in 1931, of only 167 mimeographed copies comprising the first edition, the magazine was gaining notice. In 1932, after only one year, they and the magazine had moved to New York and were underwritten by Random House. Moreover, by this time they knew all the short story writers of the day

The financial backing of Random House created conditions where subscriptions were increased to 25,000, a literary service was offered to readers, and notable new authors were continually introduced. Story is credited with the first publication and early support of a pantheon of notable authors which included: John Cheever, Carson McCullers, William Saroyan, Truman Capote, Norman Mailer, and the three authors mentioned in the introduction, among others.