Gloucester has been murdered and there's unrest and bitterness in the court. Bolingbroke accuses Mowbray of being responsible. Richard tries to mediate between them, but it doesn't work, so he arranges a trial by combat. The initial situation shows that some cracks are already showing up in Richard's government and also how lame he is at resolving problems. He can't even handle two squabbling nobles.
Instead of letting them fight, Richard banishes Mowbray and Bolingbroke and illegally confiscates Bolingbroke's inheritance when Gaunt dies. Richard was already on shaky ground when he banished Bolingbroke for accusing Mowbray of being a traitor. (On the surface, this is no reason to punish him!) So the nobles already think Bolingbroke has been treated pretty badly. When Richard goes on to disinherit Bolingbroke, things get really ugly.
While Richard is off fighting a war in Ireland, Bolingbroke slaps together an army and comes back to England for a showdown with the king. By the time Richard actually comes back to face the music, most of his subjects have either turned against him or think he's dead.
Bolingbroke kept saying throughout his campaign that he only wanted what was legally his – that is, his inheritance. That's how he won people over to his side. But by the time he catches Richard, it's clear that he can take whatever he wants, and he does. He makes Richard hand over the crown.
After losing the crown to Bolingbroke, Richard is thrown in the slammer, where he reflects on how far he's fallen and tries to figure out who he is. The real question, of course, is what is going to happen to him. Richard is trying to figure out what attitude to take toward his fall from grace. He tends to think of himself as a kind of Christ figure, surrounded by traitors and thieves. In the meantime, King Henry gets down to the business of governing and tries to get everybody to get along.
Richard is killed by Sir Piers Exton and his servants while he's locked up at Pomfret Castle. Apparently King Henry suggested that he'd like it if Exton got rid of the former king.
Henry is presented with Richard's coffin. He's not entirely happy about it, even though he feels it needed to be done. He decides to go on a pilgrimage to deal with his guilt. The fact that Henry feels guilty about Richard's death might be a good sign. Remember, Richard never actually seemed to care much about murdering Gloucester. Still, the play ends on an undeniably sad note. Whereas Gloucester's murder happened offstage, and we never even met him, the play ends with the character we've gotten to know best lying in a coffin onstage.