The Warden concerns Mr Septimus Harding, the meek, elderly warden of Hiram's Hospital and precentor of Barchester Cathedral, in the fictional county of Barsetshire.
Hiram's Hospital is an almshouse supported by a medieval charitable bequest to the Diocese of Barchester. The income maintains the almshouse itself, supports its twelve bedesmen, and, in addition, provides a comfortable abode and living for its warden. Mr Harding was appointed to this position through the patronage of his old friend the Bishop of Barchester, who is also the father of Archdeacon Grantly to whom Harding's older daughter, Susan, is married. The warden, who lives with his remaining child, an unmarried younger daughter Eleanor, performs his duties conscientiously.
The story concerns the impact upon Harding and his circle when a zealous young reformer, John Bold, launches a campaign to expose the disparity in the apportionment of the charity's income between its object, the bedesmen, and its officer, Mr Harding. John Bold embarks on this campaign in a spirit of public duty despite his romantic involvement with Eleanor and previously cordial relations with Mr Harding. Bold starts a lawsuit and Mr Harding is advised by the indomitable Dr Grantly, his son-in-law, to stand his ground.
Bold attempts to enlist the support of the press and engages the interest of The Jupiter (a newspaper representing The Times) whose editor, Tom Towers, pens editorials supporting reform of the charity, and presenting a portrait of Mr Harding as selfish and derelict in his conduct of his office. This image is taken up by commentators Dr Pessimist Anticant, and Mr Popular Sentiment, who have been seen as caricatures of Thomas Carlyle and Charles Dickens respectively.
Ultimately, despite much browbeating by his son-in-law, the Archdeacon, and the legal opinion solicited from the barrister, Sir Abraham Haphazard, Mr Harding concludes that he cannot in good conscience continue to accept such generous remuneration and resigns the office. John Bold, who has appealed in vain to Tom Towers to redress the injury to Mr Harding, returns to Barchester where he marries Eleanor after halting legal proceedings.
Those of the bedesmen of the hospital who have allowed their appetite for greater income to estrange them from the warden are reproved by their senior member, Bunce, who has been constantly loyal to Harding whose good care and understanding heart are now lost to them. At the end of the novel the bishop decides that the wardenship of Hiram's Hospital be left vacant, and none of the bedesmen are offered the extra money despite the vacancy of the post. Mr Harding, on the other hand, becomes Rector of St. Cuthbert's, a small parish near the Cathedral Close, drawing a much smaller income than before.

Question: How is Hiram's Hospital supported? 
Answer: It is supported by medieval charitable bequest.
Alternative answer: medievil charitable request by the Diocese of Barchester