TL;DR: Byzantines forced Armenian and Assyrian nobles to relocate causing the frontier of the Empire to be left unprotected and leading to them being easily invaded by the Turks. A schism between the Byzantine Church and churches of the east led to persecution of Armenians and Syriacs which caused some to welcome the invading Turks as saviors that will protect them against the Byzantines. This put the Turks as the elite of society ruling over the native population and assimilating the natives into their culture rather than the majority culture assimilating the minority. For much of Ottoman history a practice known as the blood tax saw Christians taken from their homes, converted to Islam and indoctrinated into Turkish culture and turned into the elite Janissary class of Ottoman society. Turkish nationalism rises in the final stages of the Ottoman Empire leading to persecution of Armenians, Assyrians, Syriacs, Greeks, Kurds, Jews, and many more minorities eventually leading to systematic and institutionalized genocide of these cultures in the early 20th century. Following the collapse of the Empire, the Republic of Turkey continues the path of Turkification by restricting the freedoms of non-Turks.

Firstly, I think the main indication that needs to be made is the difference between Turkic and Turkish. Turkish people are Turkic but not all Turkic people are Turkish. Those living in the country of Turkey are generally looked at as being Turkish and those people are also intermixed with the many native populations of Anatolia to the point that modern Turkish people are more closely related to Greeks and Armenians than their cousins in central asia. It is believed that Christians in Anatolia welcomed these Turkic invaders, even though they were Muslim, due to a schism between the Byzantine church and the churches to the east.

The process follows much of the same that you see when you look at nomadic groups attacking farmers and those who live in cities. Broadly speaking the Turkic entry into Anatolia started off around the 11th century due to them being displaced from their homeland in central Asia. It initially started off as small raiding groups, as would sack cities and farms of the border regions of the Byzantine Empire and Armenian Kingdoms to the east, and leading into full on migration with entire tribes and clans riding in. Religion did not have as much impact as one would expect, the Turks would attack both Christians and Muslims. The sacking of the Armenian kingdoms caused them to swear fealty to the Byzantine Empire.

What 'opened the floodgate' to allow for Seljuk subjugation of Anatolia was the Byzantine defeat at the battle of Manzikert. The Byzantine Emperor was captured, forced to sign a treaty and was then faced with civil war in his Empire. The Emperor was deposed and the Seljuk sultan was killed far away, this effectively ended the treaty. Around 1070 starts a series of Turkic migration into Anatolia that would sustain for centuries, some of these were not warriors, but nomads who don't have anywhere else to go and move into the empty frontiers of Asia Minor. Factors that could have possibly led to native depopulation of these lands includes, obviously, tremendous death and displacement caused by Turkic raids. Another factor was the Byzantines conducting large scale population transfers, meant to promote cultural uniformity in the Empire, mostly of Armenian and Assyrian nobles living in the frontiers. Consequence of the population transfer was the loss of leadership making invasion of these lands by the Turks relatively easy. Later, as the Mongols advance further to the west, more Turkic tribes are pushed into the area. Turkmen subjugation of Anatolia happens under the Sultanate of Rum (the Sultanate of Rum is succeeded by the Ottoman Empire), after sons of a former Seljuk pretender escaped their prison and made alliances with those living in Anatolia.

Although they were the minority in these lands, the Turks managed to assimilate the native populations into their culture. This could be attributed to native populations relying on the Turks for their protection, mostly due to the instability of the region, seeing the Turkification of much of the native Anatolian populations. During Ottoman times a practice known as the blood tax was introduced where the military would take sons of their Christian subjects, forcibly converted to Islam and indoctrinate into Turkish culture, the most capable of these would become members of the military elite known as Janissaries.

The Late Ottoman period saw the government seeking to assimilate their diverse population into a single core identity such as declaring Turkish as the only official language of the empire and only those who could speak Turkish can be employed by the government. Turkish nationalism was on the rise following the turn of the 20th century and the Young Turk leadership launched initiatives to even further assimilate the populations of the Empire into a uniform culture. Policies based on nationalism leads to persecution and persecution eventually culminates into the Armenian, Assyrian, and Greek genocides which sees a large percentage of native Anatolian population be systematically exterminated by the Ottoman government. The genocides of the 20th century were not the first time there was government sanctioned massacres of native populations. Those orphaned by the genocides were taken to Turkish orphanages and indoctrinated into the culture, some were recruited into the Turkish military to fight for Turkey in the Turkish-Armenian war of 1920.

The Modern Turkish state saw even further Turkish Nationalism with more attempts to Turkify the natives. Examples are forbidding those who can not read or write in Turkish from become members of parliament, excluding Greeks and Armenians from becoming civil servants and other trades, fining those who do not speak Turkish, banning non-Turkish last names, confiscation of property, changing geographical names of places and cities to Turkish names, raising taxes against non-muslims, and even to the point of changing the names of animals to remove any relation to Armenia or Kurdistan.