Note: Like a lot of scholars, Christopher Booker identifies Richard II as a tragedy, but the play also falls into the genre of history play, so be sure to go read "Genre" when you're done here.
Richard has emptied out his royal checking account and needs money to fund the wars in Ireland. He's pretty pleased with life, though: as a monarch chosen by God, he thinks he's pretty awesome, and so does everyone around him, since he only surrounds himself with flatterers. Life is good for Richard.
Richard might be said to suffer from an excess of self-esteem. He thinks he's just as great as all his yes-men say, and as a result he feels like he can do whatever he wants.
When Bolingbroke accuses Mowbray of killing Gloucester (a murder Richard seems to have ordered), Richard tries to get them to be friends. When that doesn't work, he banishes them both. When Gaunt dies, Richard is totally psyched, since Gaunt had a lot of property. He seizes it to help fund the wars.
Everything seems to be going very well for Richard! The annoying uncle who insulted him has died, leaving all his riches behind. Since Richard banished his heir, Bolingbroke isn't around to try to interfere with Richard's plan to steal Gaunt's property.
Unfortunately, at this point another uncle decides to pipe up and criticize Richard. York, who's always done what Richard told him to, tells Richard he can't take it anymore and that it's wrong to take Bolingbroke's property. Richard ignores him and goes off to Ireland to fight.
This is the point when things start to go badly for Richard. If even yes-man York is freaked out by what he's doing to Bolingbroke, then the rest of the nobles must be pretty convinced that Richard is treating Bolingbroke not just badly but illegally. Public opinion is turning against Richard, and everyone thinks Bolingbroke has a pretty good case for coming back to claim what's his.
Sure enough, Bolingbroke comes back. Richard is so far away that communication isn't really happening between him and York. The tide is turning against him. People think Bolingbroke deserves his inheritance, and a rumor starts to spread that Richard is dead. Shortly after Richard comes back, Bolingbroke captures him and Richard hands him the crown.
Richard's overconfidence in his subjects' loyalty and in his own godlike status leads him to neglect his kingdom. By the time he decides to do something about it, it's too late: Bolingbroke has total control.
King Henry gets down to the business of ruling England. Richard mopes for a while until he's finally killed by Sir Piers Exton and his henchmen.
There's some poetic justice in the way Richard dies: he's murdered in the same way Gloucester seems to have been when he was Richard's captive: as a prisoner of the king, who might or might not have directly ordered his death. The play ends with Richard's coffin onstage.