This being AskHistorians, you will no doubt not be too surprised to hear that the startling Norman success of 1066 was the product of a complex combination of factors.

To begin with, the English state itself suffered from quite a number of long-term fault-lines. It had fallen once before in the course of the 11th century, in 1016, when it became part of the North Sea empire of Cnut – and his Danish dynasty had ruled the country until the death of the second of his sons, Harthacnut, in 1042. Although Danish victory had not resulted in the large-scale importation of a new ruling class, as happened after 1066, a number of Scandinavian notables did take over positions in the Saxon hierarchy and this period must have reinforced an existing division in the country, which dated back more than a century to Alfred's reign – the existence of a semi-detached northern and eastern portion of the country, the Danelaw, which was settled by Scandinavians (how heavily remains a matter of dispute), ruled according to different customs and laws, and where a different language was widely spoken. Lack of definite information from this area in this period makes it hard to be certain exactly how loyal the Danelaw was, and how different its people felt from those of the south, but it's certainly been argued that the northern half of the kingdom was a less than wholly enthusiastic part of the Saxon state.

To the south, meanwhile, Harthacnut's successor, the Saxon king Edward the Confessor, had done much of his growing up as an exile in the Norman court. Edward had a Norman mother and, for part of his reign, a Norman archbishop of Canterbury, and he was often at odds with the most powerful of his earls, Godwin, who had been put in place by Cnut and whose family (which included his son Harold, the king who died at Hastings) was, collectively, very nearly as powerful and as wealthy as the king. All this created a difficult political situation in England for much of England's reign, with a notable flare up that came close to causing civil war in 1052.

Now, this is not to suggest that the king himself lacked power; he didn't, and Stephen Baxter's recent influential writings on his reign have stressed his ability to appoint, and remove, high nobles arbitrarily, leading to a period of considerable instability in landholding in England. By Baxter's count, one county, Oxfordshire, changed hands 17 times in the course of Edward's 24-year reign. All in all, the Saxon state that William encountered was not nearly so united or so stable as it superficially appeared to be.

On the other hand, it had at least been a kingdom that had enjoyed a long period of peace, one that dated all the way back to 1016. This meant that Saxon generals and Saxon troops had very limited experience of actual warfare. Even Harold, whose military prowess (learned in the course of fighting mostly counterinsurgency-style campaigns in Wales) was what earned him the crown on Edward's death, had never fought a pitched battle in his life before 1066.

All this was in stark contrast to the military career of William of Normandy, whose efforts to hold on to his own highly unstable patrimony meant that he had spent the best part of his three decades as duke fighting, besieging and learning how to raise, supply and command troops. The reputation that William earned in the course of these adventures built him a reputation that helped to make up for the weakness you note in your question – that Normandy was many times smaller than England. Once again, we lack the documentation to be certain, but it's typically estimated that up to a third of the army that confronted Harold at Hastings was made up, essentially, of mercenaries, drawn from other parts of what is now France to fight for a man with a considerable reputation as a leader.

Volumes have been written about what happened in 1066 itself – about the military tactics of the two armies (Norman castles and cavalry against Saxon shield walls; Norman discipline against Saxon impetuousness and so on), not to mention about the role of hard fighting and blind luck in determining the outcome of Hastings itself – the battle lasted the best part of a day and was exceptionally evenly contested by the standards of the time, and a considerable part of the eventual outcome of the campaign as a whole was determined simply by the fact that Harold and three of his brothers died in the course of the campaigns of that year, all of which meant that the only viable remaining Saxon candidate for the throne on Harold's death was Edgar Atheling, a boy of only 14. But I want to stress a couple of other things in wrapping up this response.

First, I think that writers on 1066 tend to get blinded by the specifics of the situation and of the campaigns that year, and as a result see the Norman Conquest as the product of very Saxon weakness, and very Norman strength. Take a step back, though, and it's very arguable that the sort of cataclysm that visited itself on England that year would have done for most of the other states in Europe just as easily. The death of an old king without a nominated heir was in itself enough to bring chaos, conflict and war to many states (Edward is supposed to have named Harold as his successor on his death bed, but we have only Saxon propagandists' word for that, and he certainly did not set out a clear plan for the succession well in advance). On top of that, the Saxon state faced two large-scale, separate invasions that year – a Norwegian one in the north, led by the formidable Harald Hardrada, which Harold defeated, just ahead of the Norman invasion in the south. Not one, but three major battles were fought in England that summer, and the last time so many had been waged in so short a time was 1016, a period which also resulted in regime change. Without the distraction of the northern campaign that he was forced to fight, the numerous serious losses that the Saxons incurred in the first two battles of that year, and the delay of more than a month in confronting the Normans (enough time for William to sort out his supply lines and even build himself a castle base at Pevensey), it's reasonable to assume that Harold would have had a much better chance of defeating the Norman invasion.

This would make a really good topic for a research paper. 1. There were about 4 contenders for the English throne at the time. The reigning king was Harold Godwinson, as well as his brother, Tostig Godwinson, added to that was the king of Norway, Harald Hardrada, and lastly, our friend William Duke of Normandy. In 1066, Hardrada claimed he was the rightful king of England. He had a thing for trying to take over kingdoms, as 2 years earlier he had claimed the throne of Denmark, but was reppelled. He was a battle hardened warrior who had fought in Russia and served in the varangian guard in Constantinople. He took his men to england, where he allied with Tostig, and was prepared to take the english throne. A harsh battle ensued at Stamford Bridge where the Saxons defeated the Northmen and Tostig and Hardrada were both killed in the battle, slightly weakening haralds saxon army, and leaving only two "kings of england". Now normandy was not French per se, it was in fact Viking. Normandy was founded by the Viking chieftain Rollo, who gave his alliance to the Frankish king and became of christian. Many viking warriors under Rollo became Normans and many french settled there too. Next when William made it to Hastings, where the battle ensued, some things happened. The saxon fyrds were mostly farmers who can be called upon during times of war, while most of the Normans were a professional Army. Also, the Saxon army still fought in ancient Germanic fashion, mostly on foot and in a shield wall, while the normans utilized heavy cavalry and long range archery. Another thing is that the Norman soldiers were better equipped. The Saxons still had those all too familiar Round wooden shields that are popularized by the Vikings, but also were common among most Germanic Peoples. The saxon bow was inferior, and so were the weapons. The Normans came with better armour, sharper and harder weapons, bigger shields that did better at protecting a man and a formation, most carried large long lances on horseback. The normans are often what we think of when we think of an early knight, while an anglo saxon warrior would look strikingly similar to a Norse Viking. It also didnt help that King Harald was killed in the battle of Hastings, ensuring the the remaning forces would fall into chaos and very unlikely to be able to reform successfully. From here on out, the saxons were basically fighting a gurilla war, almost like that of the Gauls fighting the Romans. Soon, the only remains of Anglo Saxon England that had ruled for 500 years were small pockets in Northumbria.