This is an important question that deserves a multi-faceted answer. To be clear, there is no single answer of how integration of conquered settlements happened, but it's useful to talk about a few examples.

Let's start with Sumerians. They had a system of city-states ruled by kings. There were frequently wars, but rarely did land change hands too significantly. It was difficult for the Sumerians to outright conquer another city-state, instead they would usually defeat a king in battle and then have him or his descendants swear fealty. This would create loose federations of city-states that could be broken by issues of succession or defeat in battle. This is largely because the city states at this time were simply not economically powerful enough to fully subsume each other [1].

Another example of this issue among city-states comes up in Greece. Sparta is well-known for its helots, which were an enslaved people from an early Spartan conquest of a neighboring city-state. Integration was challenging enough for a city-state that keeping the helots in line became a major determining factor for the Spartans going forward. Both Sparta and Athens addressed this city-state weakness through different means. Sparta would create the Peloponnesian League which is was the clear head of, and Athens created a tributary empire. Both of these allowed the city-states to exert power without having to incur the costs and difficulties of actual empire. [2][3]

Other integration examples can be seen across all empires, but two other good examples to touch on are the Egyptians and the Achaemenid Persians. The Egyptians had a strong hold on their core cities around the Nile. These cities had similar customs and systems of governance. Egypt was also much wealthier than Sumer had been. This meant that it was easier for internal conquests to consolidate strong positions and hold the entirety of 'Egypt'. Outside of that immediate sphere were Sudan, the Western Oases, the Sinai Peninsula, and what used to be referred to as the Levant. In different phases of Ancient Egypt, different strategies were put into effect to try and subdue and govern those regions. In Sudan, the Egyptians generally attempted to maintain a show of force and cow the low Sudanese into either fealty, alliance, or submission. This was because the Sudanese tended to be strong enough to resist Egyptian influence, and it was a difficult region for the Egyptians to both conquer and hold logistically. In the West, the Egyptians usually put garrisons to keep eyes on the nomads as it was not worthwhile to try and conquer either the oases or the nomads. To the East is where the Egyptian campaigns rose and fell across the very long life of the different Egyptian Kingdoms. I highly recommend reading the books that I have referenced here if you want to learn more [4][5]. Alternatively, if you want I can send lecture videos from the course that I taught on War in the Ancient Mediterranean.

The Persians stand apart as the first clear example of how conquest could happen on a wide scale. The Persians were ethnically outsiders from the entire Middle Eastern Ecosystem that was governed by Assyrians, Hittites, and Egyptians. Nonetheless they conquered and held the entire region stably for centuries. This was possible because they took a unique approach to conquest. After defeating a people, they would leave the basic tenets of the local governance in place. This meant infrastructure, local government, and bureaucracy tended to be left alone, and instead the Persians would just deposit their own ruler on top of the entire system. This system of provincial governors called Satraps was supported by an elaborate system of legitimacy and tribute. For legitimacy, the Persians did things like the Cyrus Cylinder, which appealed to the local people with their own customs and claimed that Cyrus was the legitimate ruler. For tribute, the Persians drew annual tribute from across their empire in a system that emphasized Persia's strength and their benevolence. [6][7] Critically, Alexander copied the Persian model with very minor tweaks [8].

Last we can discuss the Romans who were a bit different. The Roman model of conquest evolved during its gradual conquest of Italy. During the late Republic and the Empire, the Romans would colonize regions with veterans of their legions, adding stability to regions. They also had the logistical and bureaucratic capabilities to exert their own form of governance on the local region. One thing that made them stand apart is that the Republican system of governance gave a lot more flexibility than any monarchy, because local governors could be expected to make wider ranging choices without being a perceived threat to the overall government. Rome is such a varied entity in and of itself, Early Republic, Mid Republic, Late Republic, and the varying stages of Empire mean that no single answer here will suffice. Instead I recommend that you read the books I reference here[9][10][11]. There are many more books on the subject, message me if you want more.

[1]William James Hamblin, Warfare in the Ancient Near East to 1600 BC: Holy Warriors at the Dawn of History, Warfare and History (London ; New York: Routledge, 2006).

[2]Brian Todd Carey, Joshua B. Allfree, and John Cairns, Warfare in the Ancient World (Barnsley, South Yorkshire: Pen & Sword Military, 2005).

[3]Thucydides and Victor Davis Hanson, The Landmark Thucydides: A Comprehensive Guide to the Peloponnesian Wars, ed. Robert B. Strassler, trans. Richard Crawley, trade paperback edition (New York London Toronto Sydney: Free Press, 2008).

[4]Paul Elliott, Warfare in New Kingdom Egypt (Stroud: Fonthill, 2017).

[5]Marc Van de Mieroop, A History of the Ancient Near East ca. 3000-323 BC, Third edition (Chichester, West Sussex, UK: John Wiley & Sons Inc, 2016).

[6]Marc Van de Mieroop, A History of the Ancient Near East ca. 3000-323 BC, Third edition (Chichester, West Sussex, UK: John Wiley & Sons Inc, 2016).

[7]S. Wise Bauer, The History of the Ancient World: From the Earliest Accounts to the Fall of Rome, First edition (New York: W.W. Norton, 2007).

[8]Brian Todd Carey, Joshua B. Allfree, and John Cairns, Warfare in the Ancient World (Barnsley, South Yorkshire: Pen & Sword Military, 2005).

[9]Kurt A. Raaflaub, Nathan Stewart Rosenstein, and Center for Hellenic Studies, eds., War and Society in the Ancient and Medieval Worlds: Asia, the Mediterranean, Europe, and Mesoamerica, Center for Hellenic Studies Colloquia 3 (Cambridge, Mass.: Harvard University Press, 1999).

[10]Nathan Stewart Rosenstein, Rome at War: Farms, Families, and Death in the Middle Republic (Chapel Hill: University of North Carolina Press, 2004).

[11]Brian Todd Carey, Joshua B. Allfree, and John Cairns, Warfare in the Ancient World (Barnsley, South Yorkshire: Pen & Sword Military, 2005).