How was Islam spread among Turkish population or in historical Turkey?
How did ethnic Turkish people embrace Islam?
How was Islam spread among Turkish population or in historical Turkey?
How did ethnic Turkish people embrace Islam?
Ethnic Turks first embraced Islam when they met the expanding Arab empire in modern day Iran (and slightly to the north and east). This was where the Turks had settled, and the Arabs were conquering in the late seventh, and eight centuries A.D. The Arabs feared Turkish military prowess more than that of the longer-term "locals," and offered economic and social inducements (e.g. better education) to the Turks to support them. Part of the "package" was the Islamic religion.
By the turn of the Millenium, Arab power waned, leaving a power vacuum for the Turks to move into. These newly Islamacized Turks moved west across Iraq, into the eastern part of modern day Turkey. Around 1200 A.D. the even fiercer Mongols accelerated the process by chasing the Turks out of Iran, and into Turkey.
Short answer (in reverse order of the questions asked): The Turks were "Islamized" by the rising Arab powers when they met in Iran, and then when Arab power waned, they migrated into modern Turkey, (conquering the local Byzantine empire), making that part of the world Islamic.
When Turks arrived in what is modern-day Turkey, they were already Muslims. The Battle of Malazgirt/Manzikirt between the ancestors of modern Turks and the Byzantine Empire marks the start of this large-scale migration by Turkic tribes.
The various groups who constituted the migration were not homogeneous: there were Karakoyunlu, Akkoyunlu, Turkmen and so on. But they were Sunni Muslim by this point through long contact with the Islamic world following the Battle of Talas River in 751 in which an Arab army defeated the Chinese. This shifted the influence over Central Asia away from Christianity and Buddhism to Islam.
It's more accurate to say Turkic people as Turks tend to be one branch of Turkic family who embraced Islam. We see Muslim-Turkic interaction from the travel accounts of Ibn Batuta. He lists Turkic people into three categories of Baskurts (Living in modern day Russia), Vulgar (Turks settled in Bulgaria) and Oguz Turks (Modern day Turkey, Azerbaijan and Turkmenistan). We understand Turks believe in a religion named Gok Tengri which is not Shamanism but in fact translated as Sky God. They believe in one God only but have paganistic rituals. From modern day of Turkish accounts, the Ruler of Karahanli Empire, Saltuk Bugra Khan researched various religions from Buddhism, Judaism, Christinaity and Islam. He had special interest in Islam and according to accounts, one night he saw prophet Muhammed in his dream asking him "Is it not time for you to embrace Islam", then following that night he embraced Islam. After this Turkic population also embraced islam as they have a notion of loyalty for their Khan's.
Turkic people who lived in the middle east became Muslims or died. Many went to North European countries but the ones that stayed either converted or killed, is as simple as that. They fought bravely for 3 centuries and were usually vastly outnumbered by the muslim Arabs who for 400 years had been trying to islamsise them by the sword. If they list a battle, they were enslaved by the Arabs and Islam was drummed into them. They started learning and speaking Arabic just to be able to practice Islam like their captors. The Seljuk turks held off the muslims until they too were converted by the Arabs. The Arab kingdoms broke up like Russia and the mainly Oğuz turks formed their Islamic ottoman empire. They ironically used the same Arab tactics used to convert them of enslaving their enemies, converting them to Islam. They were accidental Muslims who today don't speak or understand Arabic and practice a religion which most don't understand.