David Home was born on what in the modern calendar is May 7, 1711 to Joseph and Katherine Home; Britain was not on the modern calendar at the time (it switched in his lifetime) so on the 'old style' calendar he was born on April 26. He was born in Edinburgh, although his family actually lived at Ninewells; he was the second son. David never really knew his father, who died when he was one year old. He was a precocious child, and had early admission into the University of Edinburgh. His family expected him to study for law, which he kinda-sorta did, but he never really had an interest; when he was supposed to be reading books on jurisprudence, he read classics. He had significant ambitions, though, and at the age of eighteen began obsessively studying philosophy. This would eventually lead to a serious breakdown in his health. He eventually recovered, to a fair extent, but while he had been a skinny kid before his health problems, he was considerably more weighty afterward. He went Bristol with some recommendation letters in an attempt to find a good mercantile position, but failed to find anything that he though suitable. It is probably about this time, however, in 1734, that he started writing his last name 'Hume' so that the English would pronounce it correctly.
From Bristol, he went to Rheims, and then to La Flèche in France, where the famous Jesuit school was, probably in part to be close to their library. He seems to have loved it; he spent three years there, writing A Treatise of Human Nature, which he published in 1738 after having returned to London. It did not make the major splash that he had hoped. At Ninewells, he started reworking the material into a more popular, essay format, which would eventually, although not immediately, be much more successful. During the Jacobite Rising of 1745, Hume was invited to be the companion of the Marquis of Annandale in England, and spent a year there. In itself this was something of a disaster (the Marquis was mentally disturbed), but connections Hume made during the visit led him to be invited as the secretary of General St. Clair on what was supposed to be an expedition to Canada but which never got further than France; he would soon after be attached to St. Clair for a while in a military embassy to Italy.
On returning from Italy, he continued to write in the essay format, as his works slowly began to pick up interest. It was in 1752, however, that his literary career would take a major turn for improvement, when he was appointed the Librarian for the Faculty of Advocates, which paid very little but gave him full access to the library. From that well he drew much, and began writing his History of England as a study of political factions. Hume's tendency not to modify his historical account to fit standard partisan lines, and in particular his active sympathy for Charles I, shocked a great many people when the first volume came out, but later volumes did quite well, and, indeed, it was primarily his work as a historian that secured Hume's literary reputation both in his lifetime and for a long time afterward.
Having finished the History, and now reasonably well-to-do, he returned to Scotland, expecting to stay there permanently, but he was invited to be secretary to the embassy in Paris. After some reluctance he went -- and discovered what it was like to be a celebrity. Only Laurence Sterne was more popular and more widely lauded. He made many French friends while there. In 1765 he became chargé d'affaires for a brief period, and when the ambassador arrived, he returned to Scotland. Despite his great enjoyment of the French, he seems to have regarded them as a bit much. He was Under-Secretary of the Northern Department for a time, and then spent his last years in Edinburgh. He became quite sick in 1775, and died on August 25, 1776.