Richard Hurd was born on 13 January 1720 at Congreve in the parish of Penkridge, Staffordshire. He was the second son of three children of John and Hannah Hurd, “plain, honest & good people”. John Hurd, “a very respectable yeoman”, rented a farm in Congreve and later a larger area of land in Pendeford, midway between Brewood and Wolverhampton. His last move was to Brewood, where he died on 27 November 1755, aged 70. Hannah Hurd died on 27 February 1773, aged 88.

Hurd's elder brother John (born in 1715) became a farmer at Hatton Grange in Shropshire. He married in 1752, but died without issue in 1792. Thomas, the youngest son, was born in Pendeford in 1725. He became a draper in Birmingham, and in 1748 married Mary Marston: their second son, Richard, became companion, secretary and diocesan registrar to Hurd whilst he was Bishop of Worcester.

Little is known of Richard Hurd's early life, but by his own account, he was educated at a “good Grammar school at Brewood”, first under “the reverend Mr Hillman, & upon his death, under his successor, the reverend Mr Budworth”. Both, he said, were “well qualified for their office, & both very kind to him”. Budworth had been Master of a school at Rugeley, also in Staffordshire, and apparently continued there for two years after his new appointment, while the schoolhouse at Brewood was being repaired. Hurd was therefore sent to Rugeley on Budworth's succeeding Hillman, and returned to Brewood with him, when work on the school was completed. Budworth, he said, “understood Greek & Latin well, & had a true tast of the best writers in those languages. He was, besides, a polite well-bred man, & singularly attentive to the manners in every sense of the word, of his scholars. He had a warm sense of virtue & religion, & enforced both with a natural & taking eloquence.” The syllabus taught by Budworth incorporated classical grammar, translation of Latin and Greek texts (with particular emphasis on Ovid and Virgil), and “natural philosophy”. On Saturday portions of “Mr Nelson's Festivals” were read out, and in Lent the boys studied their catechism. All comedies were disapproved of, and Budworth's pupils were never allowed to go and see one.