By what means did the Normans manage to rule another country with different culture, language, and structure? Was it oppression, was it keen administration? How did they do it?
The Norman Invasion and their consolidation of power can be divided into three main parts.
The first was the initial invasion, decided by the Battle of Hastings. This battle effectively eviscerated the existing ruling apparatus and allowed William to insert himself in as King. However, this battle, despite being decisive against the Godwin family (King Harold's family), actually didn't decide anything right away. It did, however, result in significant and immediate confiscations of lands held by those killed at the battle.
The second part was the period from 1066 to about 1076, was a power struggle between the Earls and the new 'King'. It's important to note that England was a realm filled with very powerful Earls, and immediately after Harold's death a succession of them attempted to retake the crown the same way that Edward had only a generation earlier. A series of revolts by these earls occurred, roughly in a pattern outward from London, and each was crushed in turn. Unified resistance was never a problem, but rather, foreign support from the Danish and Scottish was the real issue, and over the following ten years William managed to defeat these outside threats to his power, as well as erode the power of the Earls who revolted in turn. Undermining these men was a lack of unity and competing interests between foreign powers. If the Danes and Scots had united, or all the Earls united, William might have had a more difficult time, but everyone was basically trying to be the one holding the reigns of power when William was defeated.
The final part of this is how William consolidated his power. The first obvious step was the seizing of estates (as mentioned in the first part above), but the way this was done was pretty interesting. All land seized from rebellious Earls wasn't simply handed over to members of William's entourage, but rather, broken up into often highly divided geographically smaller pieces. In addition, a great number of castles were built in these newly subdued areas, helping cement Norman influence. By giving out these smaller pieces of land, he was gauranteeing loyalty of his new nobles as well as reducing their ability to effectively cause trouble for him.
With the Anglo-Saxon nobility crushed and replaced by more loyal Normans who were less able to challenge his authority, England's level of centralization in the Normal period exploded compared to what it was under the Anglo-Saxons and Danes. England also faced fewer external threats after 1076, with the Scots and Danes both humbled during William's campaigns to halt their support of rebellious Earls. This allowed William to not only leave for Normandy after 1076, but to also rarely return. It also allowed him to enact the survey and levy that is now known as the Domesday Book only ten years later.