Richard was educated at St Andrews University, but left without taking a degree. He intended when a young man to take holy orders, but his father opposed this, and so he entered his father's firm. He married Eleanor (1820–1891) daughter of the major shipowner, John Brocklebank, of Hazelholm, Cumberland on 27 August 1840. They had six children, of whom two died in infancy. Little is known of Moon's early adult life, but he appears to have withdrawn from the family firm by 1851. However, his family had invested early in railway shares, and in 1847 Richard Moon was elected a director of the London and North Western Railway Company (LNWR). He became chairman in June 1861, holding that position until he retired in February 1891.
The London and North Western Railway Company came into being on 16 July 1846 by the amalgamation of the Grand Junction, the London and Birmingham, and the Manchester and Birmingham railway companies. The chairman of the new company was George Carr Glyn. The marquess of Chandos became chairman in 1853. He was forced to resign in 1861, and was briefly succeeded by Admiral Moorsom, who died in May of that year, and Moon was elected chairman. Since joining the board in 1847 he had established a reputation as an outstandingly able administrator with little time for the senior executives of the company. He brought about the resignation in 1858 of Captain Mark Huish, the first general manager of the new company.
Moon was essentially conservative in his outlook, but could be innovative when he thought it in the best interests of the company. He certainly ran it very tightly, constantly looking for means of cutting costs, but he could also spend lavishly if this appeared to him to be justified—for example, on the expansion of the works at Crewe. Annual receipts of the company rose from £4.3 million in 1841 to £11.8 million in 1891, and the dividend from 4.25 per cent to 7 per cent, while the network grew from 1030 miles to 1830 miles. The company was employing 55,000 men in 1885, and was, at that stage, the largest joint-stock company in the world. Under Moon's guidance it became famous for the punctuality of its trains, the courtesy of its staff, and the creation of two new towns, Crewe and Wolverton; and in all of this he took a close personal interest.
Both the Grand Junction and the Manchester and Birmingham Railway Co. had reached Crewe before the amalgamation. The town began as a wayside station in the parish of Church Coppenhall, in Cheshire, in 1837. It was the Grand Junction that opened railway works there in 1843. The company set about building a new town, and this was continued after the amalgamation. It was administered at first from Euston, but the Crewe local board was formed in 1860, and the town was incorporated in 1877. The company provided everything: housing, water, gas, churches, and schools. It presented the municipal park to the town in 1887, the year of Queen Victoria's golden jubilee, when Moon was created baronet and became the first freeman of the town. Bessemer steel works were opened in 1864 and four years later the Siemens–Martin open-hearth furnaces were added. After 1864 carriage building was concentrated in Wolverton and locomotive building at Crewe, where locomotives were manufactured from raw materials, everything being made on site.
The London and Birmingham Railway Company had acquired 8 acres of land at Wolverton, a small village and parish in Buckinghamshire, in 1837. It began to build houses in 1839. Further land was bought in 1840, and by 1847 a new station had been built, and new streets laid out. As at Crewe, the company provided everything: housing, gas, a building society, a savings bank, market house, shops, and church, and opened a park in 1885. The company itself withdrew from building houses in 1860, preferring to lay out the plots and control the type and standard of those built.
Richard Moon retired from the board of the LNWR on 22 February 1891, his wife having died on 31 January. He died at his home, Copsewood Grange, Stoke, Warwickshire, on 17 November 1899. His eldest son, Edward, had died in 1893, and so he was succeeded in the baronetcy by his grandson, Cecil Ernest Moon, born in 1867.
Sir Richard Moon was described by his obituarist in The Times as ‘the hardest of hard workers and the sternest of stern disciplinarians’. He was said to combine ‘an assured confidence in the correctness of his own judgement with an autocratic spirit which hardly recognized the possibility of that judgement being criticized by others’. At the same time he was of ‘a singularly retiring disposition’ (The Times, 18 Nov 1899). He was Conservative in his politics, and remained a devout Anglican throughout his life.