Well there are a couple of different ways you can have this transfer of power (and this is by no means an exhaustive list).

You can have a complete territorial wipeout/genocide, population exchange, what have you where you're bringing in your own people and the old people are gone from the land. In such a case, you're really only bringing over the problems you already had, but the support as well.

You might chose to enslave the locals, which again, helps your problem of trying to win them over, but you do then risk a revolt.

You could try to intermarry, combine local and introduced populations.

Or, you can simply keep existing power structures in place with a new figurehead at the top. Instead of fighting for Emperor so and so, you now fight for me, when I call for you, you're marching for me. I might make you give up a certain amount of your army, or take some of your sons hostage where they will live in luxury in my home city just so you know there will be strong consequences if you try anything, but overall you get to keep the same local politicians, the same local bankers, businessmen, and the guy who ran the city previously now just listens to me, or maybe another big and respected member of the population who everyone already likes. You maintain your culture, your language, your art, and so forth.

Under the latter system, the common person probably wouldn't notice much of a change, but the more the conquering person interferes, the more effect it will have on you -- but also the greater chance you have of revolt, unless you just kill everyone. But if you kill everyone, you lose people to work the land, businesses that already thrived and could make money for you, specialised military units, and so on and so forth.