Richard informs us in the first scene that things have swung round to his family's side, but we immediately learn that he doesn't value family, as he plans to drive a wedge between his two brothers, Edward and Clarence. We also learn a lot about Richard's character: not only is he responsible for having Clarence imprisoned, he's incredibly two-faced, letting Clarence believe he'll support him in this time of need. We learn that Richard has some plans to "bustle" in the world (though we're not yet sure what that means), and we know he seems pretty ruthless, likely to do anything necessary to reach his goals.
Richard is far removed from the throne. Before he can have a legitimate claim to be king, his sick brother will have to die, and he'll have to kill his other brother Clarence and murder Edward's two sons. Besides Richard's personal problems, the we learn about the strife in the York family. Edward's wife (Queen Elizabeth) and her family are enemies to Richard.
Then enters Queen Margaret, widow of the former King Henry VI. Margaret's curses frame all these problems for us: she wishes everyone to anticipate all the treachery and death that will follow, and her curses are prophetic. Queen Margaret adds a third orbit to the play's central conflicts: Richard's got his own issues, he's got issues with the family, and the family has broader issues within the greater scheme of England's political history.
In this thicket of problems, Clarence's murder pushes Edward over the edge. As he dies and the women wail, the question arises of who will replace him. The throne is getting a little closer for Richard, and we're assured that his actions will only become more devious and bloody.
The citizens' scene, Act 2 Scene 3, frames the difficulty of the approaching situation. Though Edward's young son should be secure in the throne for now, the citizens note that the prince's youth makes him more vulnerable to power politics than they're comfortable with. The citizens also note that the enmity between Richard and the queen promises to complicate the prince's security. Prince Edward is the son of Queen Elizabeth, and Richard has been named his protector, the advisor acting in his stead while he's still young. England is definitely not safe in this situation, and everyone is worried.
Richard meets his nephew and begins planning how to exploit his position of power. He starts sending out feelers to see who would support him if he made a grab for the crown. He's growing more vicious, ready to murder anyone who stands in his way. While Richard is effectively able to kill Hastings, Buckingham has little luck in trying to convince the people that Richard should rightfully be their king.
So Richard is on the throne, and we know that nothing good can follow. Richard's taking of the throne may have been a bit anti-climactic, but it's fascinating to watch the way he fights to keep the crown. Here he becomes rather coarse in his cruelty: he orders the princes to be murdered and is gleeful to hear they've been smothered and disposed of. Growing even more bloodthirsty, as the first reports come in about a force gathering to fight him, Richard fiercely declares himself ready to battle "the traitors."
With the princes out of the way and his wife Anne suddenly and mysteriously dead, Richard makes a move to take the young Elizabeth's hand in marriage, which would seal off all avenues for another challenger to the throne. Freshly cursed by his own mother, Richard is utterly without shame. He thinks he's won Queen Elizabeth's consent to marry her daughter. We're left in suspense as to whether Queen Elizabeth will actually help Richard but are quickly distracted by the news that Richmond is on his way.
Richard, fierce as he may be, begins to seem flustered and confused, but no less bull-headed in his battle plans. We're unsure whether he can secure a wife or hold up under the stress of battle. Ultimately we know Richard will be defeated, but we're still unclear how that will happen. Richard is still scheming, but we have hints that he might be losing his wits.
Once Richmond has the blessing of the dead and Richard receives their damning curses, it's clear that Richard will lose on the battlefield. Throughout the play Richard has been cursed by others, but the true sign that Richard's doom is upon him is a rare moment of self-doubt. Waking from his dream, Richard seems unsure of who he is and how he feels about himself. Until now Richard has never doubted himself or his ability to manipulate others. No one can ever be sure of him – except himself. Now that it's clear that he's lost touch with himself, he has no one left in his court. He knows this, and he prophetically declares, with his characteristic cavalier attitude: "let us to it pell-mell, If not to heaven, then hand in hand to hell." Richard's assurance about keeping the crown has cracked. Warned by all the ghosts of his past, he irreverently faces his own death.
Richard concludes the play without ever repenting. He fights for the fruits of his evil to his last breath. He meets his end with a strange violence that we can't help but admire: he was determined to prove himself a villain, and he ends a villain. Even if we can't empathize with Richard's evil aims, in the end we've got to respect him for sticking to his guns. Everything ends well enough: Richard's evil is vanquished and the kingdom is protected from usurpers. And since the whole play has had us following Richard's evil, we derive some satisfaction in watching our protagonist reach his inevitable end on his own terms.