This is a very interesting question! If I may, I'd like to offer some insight from a Welsh perspective (as I am prone to do!) to illustrate how the Normans were so blindingly successful at what they did. Much of their continental brand of colonialism applies equally to Wales as it does to England too. I won't offer anything on the Norman military conquest of Wales, given that your question deals with how William was able to supplant the native nobility after the success of his campaigns.

The reality was that there was relatively little bloodshed once William had extended through south Wales after Hastings, largely as a result of some shrewd earldom appointments and prolific castle building. Given that Wales was a fragmented, pre-feudal society at the time of the invasion, they didn't really need to wander around killing people to achieve their goal of subjugation. All they did in essence was import a continental European way of life, without taking no for an answer, that became accepted as the new normal.

Gwyn Williams says that the Normans, and William in particular, "made the Welsh a European people" but I think it goes much further than that. They imported a feudal economy, and with it, a whole new system of governance that embedded itself within Welsh society (though there were important topographical considerations that I'll touch on in a bit). Think about what William introduced to Wales (or at least played a part in facilitating):

• A currency-based economy
• European forms of worship
• Monasteries
• Intercontinental trade
• Castles, castles and more castles!
• Feudal governance

Also - and this is absolutely crucial to understanding how successful William was in Wales - he made associations with the European Church and the traditional Welsh forms of worship through events such as his pilgrimage to the tomb of St David (which was worth half of a pilgrimage to Rome, according to Pope Callixtus II).

William also learned where to stop, and understood where to get the most bang for his conquering buck, so to speak. He didn't bother advocating for further excursions en masse into mid and north Wales (they wouldn't come until the English conquest of Wales by Edward I in 1277). The Normans recognised that the Welsh economy was most valuable throughout what came to be known as the Marches, which is essentially modern day South Wales. They filled this area with Angevin trade and, again, legitimised their rule without the need to constantly subdue the local populace or fight a running guerrilla war as was seen later on further north.

So what happened to the old South Wales nobility? They pretty much gradually became Anglo-Norman (though to varying degrees per house) through a sustained period of unashamed rutting! William's cultural victories can largely be attributed to Norman attitudes towards intermarriage, which they were fierce proponents of! They were constantly at it, for want of a better phrase, and had no qualms about combining their own cultural practices with those of an indigenous people. The Normans created a whole new Anglo-Norman nobility in Wales. From this class emerged prominent Welsh cultural icons such as Gerald of Wales - whose documented travels through Wales became the stuff of legend - and Nest ferch Rhys, although cultural lineage has been subject of debate in Wales, and still very much is.

In terms of how Welsh people viewed William and his Lords, despite all the political manoeuvrings and wholesale changes to the Welsh economy and landscape, we tend to ignore what life would have been like for a Welsh subsistence farmer once William had made his way over the border from England. In all likelihood, all it meant for the common man or woman was seeing a different face trot through every now and then, speaking a different language and carrying a funny shaped shield! It's easy to get obsessed with a top-down view of history, but in all probability, common folk would barely have noticed any difference outside of populous coastal regions of which there were very few in wales, or unless you lived within eyesight of a castle - a tool the Normans used to profound effect.

Edit: Spelling

Source - Gwyn Williams (1985), When Was Wales?, pp. 62-170.

There will always more to be said, I'd first recommend to check the following two previous posts answered by /u/BRIStoneman:

• After the Norman conquest of England, were there any uprisings by Anglo-Saxons?
• How Anglo-saxon is the British nobility?