Richard received his early education at Adair's school at Fermoy, and, after serving an apprenticeship to a surgeon in Ireland, came to London to pursue the more scientific part of his professional studies at the Aldersgate School of Medicine, under the supervision of his brother Jones. He afterwards went to Paris, where he attended the lectures of James Richard Bennett, a private lecturer on anatomy and an Irish friend of his father. In 1828, when Bennett was appointed a demonstrator of anatomy in the newly constituted school of the university of London (now University College) Quain assisted his patron in the duties of his new office.
Richard received his early education at Adair's school in Fermoy, and after serving an apprenticeship to a surgeon in Ireland, came to London to pursue the more scientific part of his professional studies at the Aldersgate School of Medicine under the supervision of his brother Jones. He later went to Paris where he attended lectures on anatomy by James Richard Bennett, a private lecturer who was also an Irish friend of his father. In 1828, when Bennett was appointed as a demonstrator of anatomy in the newly constituted school of the University of London (now University College), Quain assisted his patron in the duties of his new office.