Answer by taking a quote from the following article:

Harold Frederick Shipman (14 January 1946 - 13 January 2004) was a British general practitioner and one of the most prolific serial killers in recorded history. On 31 January 2000, a jury found Shipman guilty of fifteen murders for killing patients under his care. He was sentenced to life imprisonment with the recommendation that he never be released. The Shipman Inquiry, a two-year-long investigation of all deaths certified by Shipman, which was chaired by Dame Janet Smith, examined Shipman's crimes.

Shipman hanged himself in his cell at Wakefield Prison at 06:20 on 13 January 2004, on the eve of his 58th birthday, and was pronounced dead at 08:10. A Prison Service statement indicated that Shipman had hanged himself from the window bars of his cell using bed sheets.  Some of the victims' families said they felt cheated, as his suicide meant they would never have the satisfaction of Shipman's confession nor answers as to why he committed his crimes. The Home Secretary David Blunkett noted that celebration was tempting, saying: "You wake up and you receive a call telling you Shipman has topped himself and you think, is it too early to open a bottle? And then you discover that everybody's very upset that he's done it."  His death divided national newspapers, with the Daily Mirror branding him a "cold coward" and condemning the Prison Service for allowing his suicide to happen. The Sun, however, ran a celebratory front-page headline; "Ship Ship hooray!" The Independent called for the inquiry into Shipman's suicide to look more widely at the state of Britain's prisons as well as the welfare of inmates. In The Guardian, an article by Sir David Ramsbotham (former Chief Inspector of Prisons) suggested that whole life sentencing be replaced by indefinite sentencing as these would at least give prisoners the hope of eventual release and reduce the risk of their ending their own lives by suicide as well as making their management easier for prison officials.  Shipman's motive for suicide was never established, although he had reportedly told his probation officer that he was considering suicide to assure his wife's financial security after he was stripped of his National Health Service (NHS) pension. Primrose Shipman received a full NHS pension, to which she would not have been entitled had Shipman lived past age 60. Additionally, there was evidence that his wife, who had consistently protested Shipman's innocence despite the overwhelming evidence, had begun to suspect his guilt. Shipman had refused to take part in courses leading toward a full confession of his crimes, leading to temporary removal of privileges, including the opportunity to telephone his wife. During this period, according to Shipman's cellmate, he received a letter from Primrose exhorting him to "tell me everything, no matter what". A 2005 inquiry found that Shipman's suicide "could not have been predicted or prevented", but that procedures should nonetheless be re-examined.

How did he die?
Shipman had hanged himself from the window bars of his cell using bed sheets.