Warning: wikipedia contains spoilers
The play begins with the Earl of Warwick (Richard Neville, Earl of Warwick) presiding over a dispute between Richard, Duke of York and the reigning King Henry, in the course of which Henry agrees to make York his heir. The Queen, Margaret of Anjou, makes it clear that she will not agree to this, and declares war on the Yorkists, with the assistance of the young Lord Clifford and other supporters, including her son, Edward, Prince of Wales.
At the Battle of Wakefield, the Yorkists are defeated, and there follow some of the bloodiest and most heart-rending scenes in all of Shakespeare, as Clifford murders York's young son, the Earl of Rutland. (In reality, Rutland was seventeen and had taken full part in the battle.) Margaret and Clifford then taunt the duke of York before killing him. The Earl of Warwick now takes York's eldest son, Edward (King Edward IV of England) under his wing. At the Battle of Towton, they take revenge on Margaret's army, and Clifford is killed. Following the battle, Edward is proclaimed king, and his two brothers, George and Richard are created Dukes of Clarence and Gloucester respectively. Richard is already showing signs of turning into one of Shakespeare's most famous villains, though in reality he was less than ten years old at the time of the battle.
Warwick turns against Edward when he marries Lady Grey (Elizabeth Woodville) without his knowledge, and he changes sides, joining Queen Margaret and allowing his daughter to marry the Prince of Wales, her son. The Duke of Clarence goes over to Warwick, marrying his other daughter, and Edward IV is taken prisoner. He is rescued by his brother Richard and the faithful Lord Hastings. King Henry VI has been restored to the throne, and the young Earl of Richmond (the future King Henry VII of England) is given a prominent part in the action, as he is shown going into exile in France to escape the Yorkists. Edward defeats and kills Warwick at the Battle of Barnet. In a subsequent battle, he kills the Prince of Wales and captures Queen Margaret. Richard of Gloucester begins his campaign to remove all obstacles in his path to the throne by murdering King Henry VI who is a captive in the Tower of London. Henry prophesies Richard's career of villainy and his future notoriety. However, King Edward's wife has just given birth to a son, the future King Edward V of England, and this is how the play ends.