For example, how where they convinced to give their taxes to the now overlord and previous enemy, or to fight against their previous kingdom? How loyal were the people? What if the new kingdom had a different language?
Religion played a large role in this. Seeing as through the vast, vast majority of the Western world was strictly Christian throughout this period, a ruler could successfully associate himself with religion and God through a variety of ways. Charlemagne, for example, placed his throne in the Church of his palace, and elevated it above his subjects so as to give the impression of him being ordained by God, a channel if you will. Rulers could additionally promote a notion knows as the 'Cult of Saints', a concept promulgated by historians such as Geary. Geary notes the association between relics, saints, and the cohesion this could bring to society. Charles the Great's reforms during the 9th century attempted to centralise and institutionalise this kind of worship, thus intertwining the notions of worship and religion with government and his kingship. Religion had the ability to transcend politics to a certain extent.
All this being said, medieval conquest, or conquest in general for that better, was in general not simply motivated by expansionist policies. It required a suitable casus belli for war to be legal and justifiable, and this was usually found in areas that were previously disputed anyway, thus resulting in areas which were already somewhat supportive of any new regime or government. Alternatively, as can be seen in William the Conqueror's invasion of Saxon England, displays of power in the form of motte and bailey castles, later developing into Burghs, acted both as administrative and military centres of power. Such displays of power were not necessarily incorporating in nature, but were successful deterrents for not complying with the government, whether this be taxation, levying etc.
Source: Patrick Geary, "Furta sacra: Thefts of Relics in the Central Middle Ages".