William, Duke of Normandy, was born in 1027, the bastard son of Duke Robert the Magnificent (also known as Robert the Devil) and his mistress Herleva (Arlette). In 1064, he was named heir to the throne of England, at least by his own account, based on the fact that a paternal aunt was the mother of King Edward the Confessor, and the two men were cousins. According to William, Harold Godwinsson, Earl of Wessex, carried the news to him, and swore a holy oath to support his claim, and to follow him.
However, on Edward's deathbed, in January 1066, Harold claimed that he commended the country into his (Harold's) care. Probably knowing this claim to be shaky at best, Harold had himself crowned king of England the day following the death of The Confessor.
Harold was excommunicated by the Pope, for violation of his holy oath. Oddly, William had also been excommunicated for marrying his cousin Matilda, but had been reinstated on the succession of a new Pontiff.
With this support, invasion from Normandy was inevitable, and for several months, Harold kept his militia in readiness. However, as the summer wore on and no assault came, supplies were used up, and eventually, Harold had to stand down much of his force.
It was at this point that a third contender for the English throne, Harald Hardrada, king of Norway made a move to capture it. His claim was based on an agreement with Harthacut (Hardecanute), the last Danish king of England, who preceded Edward on the throne. In mid-September Hardrada landed an invasion force in Yorkshire, and Harold was compelled to lead his forces north to counter this threat. Making excellent time, the English army marched to Yorkshire and engaged the Norsemen at Stamford Bridge, outside York on 25 September, taking them by surprise with the speed of his response. The invaders were routed, and both Hardrada and Harold's brother Tostig, Earl of Northumberland (who had joined with the invaders), were killed. The remaining forces took to their boats, and headed, beaten, back to Norway. The scale of Harold's victory can be measured by the fact that only 10% of the invading force returned home.
However, as the English army was recovering, news came that William had landed at Pevensey in Sussex. Harold had to subject his troops to another forced march along the length of the country to meet the Normans, a far more formidable foe.
The armies were about the same size, (4000-7000), but the English force was made up of peasants and poorly trained infantry, while the Norman force was purely fighting men, and contained archers and cavalry, both of which the English lacked. In addition, Harold's troops were tired, while William's were fresh.
On October 13, Harold positioned his force on a ridge, 5-10 miles outside Hastings, giving himself the advantage of higher ground. On the morning of the following day, after the customary jeers and insults were exchanged, the armies engaged. Harold's troops made a shield wall, to protect themselves from arrows, but even so, they were tightly packed enough to make easy targets for the Norman archers, and as the bowmen began to fall, William brought his cavalry to the fore, to charge the English shield-wall. Throughout the day, he alternated cavalry and archers, wearing down the English, who fought hard, and inflicted heavy casualties on the French. Towards the end of the day, William feigned two retreats. The English left their protected position to give chase, and the Normans turned and charged them. The result was carnage for the English. Harold and both his brothers were killed, along with much of the English aristocracy -- though it is very unlikely that the figure with the arrow in its eye depicted on the Bayeux Tapestry is Harold. Reports from the time say that, in fact, Harold was so badly hacked and disfigured that his mistress had to identify him.
William moved on to London, and was crowned king on 25 December 1066, his appellation
"The Bastard" giving way to a new title "The Conqueror".
Transition to Norman rule wasn't easy, however. Revolts by what remained of the English aristocracy were common (one of the best known being that of Hereward the Wake) through until 1075. Castles were built throughout England to act as bases to subdue the periodic rebellions.
At the time of the Conquest, the English political system was well developed and effective, and the Normans maintained most of it, simply superimposing a level of military feudalism on top, in which the English thegns, clergy and administration were replaced by Norman, and the language of law and literature shifted from Saxon British to Norman French and Latin, evidenced by the fact that the modern English language has around 60% of its vocabulary with roots in one of those two languages.
Norman rule of England is said to have continued until the ascension of the Plantagenet, Henry, to the throne in 1154, William being succeeded on the throne by his sons William Rufus, and Henry and his grandson, Stephen. However, all the reigning monarchs of England to the present have been descended in one way or another from this line (albeit in a convoluted manner), which supplanted the Danish and Saxon rulers.