Short answers, pulled from the story.
Henry Tudor, Earl of Richmond, won the Battle of Bosworth Field on the 22nd of August 1485, defeating and killing Richard III. Historians consider the battle to mark the end of the Plantagenet dynasty and the beginning of the Tudor dynasty, which would rule England for more than a hundred years.
Richard III was killed after leading a mounted charge across the battlefield to reach Henry Tudor directly. The Burgundian chronicler Jean Molinet recorded that a Welshman struck the death-blow with a halberd while Richard's horse was stuck in marshy ground. Analysis of Richard's skeletal remains found eleven wounds, nine of them to the head, including a blade wound consistent with a halberd that sliced off part of the rear of his skull.
Lord Thomas Stanley and Sir William Stanley brought a combined force of between 4,000 and 6,000 men to Bosworth but initially held back from the fighting while deciding which side to join. When Richard III led a charge that separated him from his main army, William Stanley rode to Henry Tudor's aid, surrounding Richard's group. Their intervention was decisive in Henry's victory.
The precise location is disputed. The Bosworth Battlefield Heritage Centre was built in 1974 on Ambion Hill, south of Market Bosworth in Leicestershire, but subsequent surveys challenged this. Geological work by the Battlefields Trust between 2003 and 2009 led archaeologist Glenn Foard to conclude the battle was fought approximately 2 miles south-west of Ambion Hill, near the Fenn Lanes Roman road close to Fenn Lane Farm. Historic England has re-drawn the registered battlefield boundary to reflect this finding.
On the 12th of September 2012, archaeologists announced the discovery of a skeleton under a car park in Leicester, which they suspected was Richard III. On the 4th of February 2013, DNA testing convinced Leicester University scientists beyond reasonable doubt that the remains were his. On the 26th of March 2015, they were ceremonially reburied in Leicester Cathedral.
Shakespeare made Bosworth the climactic battle of his play Richard III, preceding it with three scenes and more than four hundred lines of dramatic buildup, though the battle itself is covered in only five stage directions. He invented a single combat between Richard and Henry Tudor, borrowed the idea of Henry using decoys from the historical Battle of Shrewsbury in 1403, and kept Margaret of Anjou alive beyond her actual death in 1482 to deliver prophecies. His primary sources were the chronicles of Edward Hall and Raphael Holinshed, which drew heavily on the pro-Tudor historian Polydore Vergil.