Craig was born in Macosquin, County Londonderry, Ireland, where his father was an Anglican minister, on 6 November 1843 and he was educated at Portora School, Enniskillen.
[1] In 1874 Craig moved to London, where he became a private tutor for the Civil Service and Army entrance examinations, and university matriculation.
[1] It had been Craig's intention to expand his glossary for separate publication, but this was unfinished at the time of his death.
In 1901 he succeeded Edward Dowden, a friend from his student days at Trinity, as general editor of the Arden Shakespeare series, while continuing to teach English literature to private pupils from his rooms at 55a Gloucester Place, London.
Among his pupils was the future novelist and lecturer in English literature Natsume Sōseki, who had been sent to London on a scholarship from the Japanese government.