Garnett was born in Brighton, England, the sixth of the eight children of the solicitor David Black (1817-1892), afterwards town clerk and coroner, and his wife, Clara Maria Patten (1825-1875), daughter of George Patten. Her brother was the mathematician Arthur Black, and her sister was the labor organizer and novelist Clementina Black. Her father became paralysed in 1873, and two years later her mother died, from a heart attack after lifting him from his chair to his bed. She was initially educated at Brighton and Hove High School. Afterwards she studied Latin and Greek at Newnham College, Cambridge, on a government scholarship. In 1883 she moved to London, where she worked initially as a governess, and then as the librarian at the People’s Palace Library. Through her sister, Clementina, she met Dr. Richard Garnett, then the Keeper of Printed Materials at the British Museum, and his son Edward Garnett, whom she married in Brighton on 31 August 1889. Edward, after working as a publisher’s reader for T. Fisher Unwin, William Heinemann, and Duckworth, went on to become a distinguished reader for the publisher Jonathan Cape. In the summer of 1891, then pregnant with her only child, she was introduced by Edward to the Russian exile Feliks Volkhovsky, who began teaching her Russian. He also introduced her to his fellow exile and colleague Sergius Stepniak and his wife Fanny. Soon after, Garnett began working with Stepniak, translating Russian works for publication; her first published translations were "A Common Story" by Ivan Goncharov, and "The Kingdom of God is Within You" by Leo Tolstoy. The latter was published while she was making her first trip to Russia in early 1894. After visits to Moscow and Saint Petersburg, she traveled to Yasnaya Polyana where she met Tolstoy; although the latter expressed interest in having her translate more of his religious works, she had already begun working on the novels of Turgenev and continued with that work on her return home. Initially she worked with Stepniak on her translations; after his untimely death in 1895, Stepniak’s wife Fanny worked with her. Over the next four decades, Garnett would produce English-language versions of dozens of volumes by Tolstoy, Gogol, Goncharov, Dostoyevsky, Turgenev, Ostrovsky, Herzen and Chekhov.