Different rulers handled this differently. There were different governmental/societal structures in different times and places that would govern or limit the options of some, and there were a whole host of outside factors they had to consider when deciding their strategy. The time period you're asking about spanned a long period of history and included many different cultures. Feudal rulers just wouldn't have the options that absolute monarchists would have. The Holy Roman Emperor would have far fewer options than the Roman emperor. Etc.

The most hands-off approach would be to leave local rulers in place and let them do whatever they wanted as long as they collected any taxes/levies you ordered. This has the advantages of being the easiest to organize and maintain, and it avoids any potential problems with angering the local powers and having to fight them or upsetting pre-existing social structures that could disrupt production/commerce and reduce or eliminate tax profits. Sometimes the rule of that place would be in name only and the ruler wouldn't have any real power to tax or levy troops from that region, but it was good enough for them to just have the title for propaganda.

A slightly less hands-off approach would be to send your own local ruler to that place to look after it. Aside from a small cadre of personal bodyguards and servants you wouldn't need to drain your resources to control this place. This is only an option for a place hats thoroughly pacified and poses little to no danger of rebellion. Alternatively, you could replace the local leaders with other local leaders more likely to act as you want, or you could send your own man to "advise" the leaders and enact your wishes while keeping the power nominally in the hands of the local rulers.

If a territory might give you problems, you'd want to split off a part of your army and send it there. This could be a small, token force to just remind everyone who's in charge and provide a firm cause belli to respond if they're attacked (like US troops in South Korea), it could be one or two units of the army (like the Romans did for places like Britain by sending a legion), or it could be a very significant chunk of your army to keep a lid on things until you felt more secure in your ownership of the territory (they could be permanent if you never did feel secure). Most times and places in Europe wouldn't have a permanent standing army, though, so this wouldn't be an option for them. Also, it would be very expensive and consume a lot of resources so this territory would have to really be worth it. Also, if there were significant threats to your home territory, you couldn't afford to send large amounts of troops away from your homeland without compromising your defense.

The most extreme case would be to just move your court there. Change the capital to the new territory instead of the old. If your home territory is very secure and the new territory is rich, this could be a good move.