Richard II was actually not a horrible king, but he lacked one essential quality: the ability to understand how to compromise among competing concentrations of power. He naively believed that absolute power should, and therefore did, lie with the King, i.e., himself. It did not. In England and in anywhere else, any leader rules by consent of multiple social and economic power bases. Piss off enough of those bases, and you're out.
In 14th century England those bases were the established nobles, many of whom he sidelined in favour of his friends. When they pushed back, he pushed harder, and the ultimate crisis came when he imprisoned and murdered the most powerful lord of the realm, the Duke of Gloucester, and exiled two more. He was childless at the time (his wife was just 13). The putative heir to the throne was a great-nephew, but the real threat was another nephew, Henry Bolingbroke, whom he also exiled.
Exiling a group of powerful nobles to a wealthy foreign country not entirely devoted to your interests is a very bad idea. Bolingbroke gathered a force, returned to England, and deposed Richard without encountering any resistance: nobody would lift a sword in favour of the King. Richard was captured and taken to London, where crowds threw garbage at him. He renounced his crown before Parliament and was imprisoned in Pontefract Castle, where he died around the second week of February, 1400, either by starvation or murder. Henry Bolingbroke became Henry IV.
In some versions of the tale, including that of Raphael Holinshed, a chronicler of the 16th century and source for Shakespeare's play, Richard II is murdered, and very dramatically at that:
"Sir Piers entered the chamber, well armed, with eight tall men likewise armed, every of them having a bill in his hand. King Richard perceiving this, put the table from him, and stepping to the foremost man, wrung the bill out of his hands, and so valiantlie defended himselfe, that he slue foure of those that thus came to assaile him. Sir Piers being half dismayed herewith, lept into the chaire where king Richard was wont to sit, while the other foure persons fought with him, and chased him about the chamber. And in conclusion, as king Richard traversed his ground, from one side of the chamber to another, and comming by the chaire, where Sir Piers stood, he was felled with a stroke of a pollar, which Sir Piers gave him upon the head, and therewith rid him out of life, the 14th of February, 1399. It is said that Sir Piers of Exton, after he had thus slain him, wept right bitterlie, as one stricken with the pricke of a giltie conscience, for murthering him whom he had so long time obeied as king."
And here is why I've included Richard II's death here: Sir Piers of Exton is my ancestor. The name "Exton" is given to many of the men in my family on my mother's side in commemoration of this.
Sources: Wikipedia; Fox, George, The History of Pontefract, in Yorkshire, 1827.