It is a very complicated and a very long process. Compulsion, voluntarily conversion and socio-political dynamics acted behind this historical development. The first conversion in Turkish history took place in the northern steppes of the Caspian Sea, khan of Volga Bulgarians - whom were regarded as Turkic people - used Islam against Khazarians who were converted to Judaism against both the Caliphate and the Byzantines. Another example is when the Arab and Chinese armies fought against each other in 751, some Turkish clans in the Chinese army changed their sides during the battle and fought for the Arabs because there was a traditional hostility between the Chinese and the Turks in Middle Asia. So, we can see conversion into Islam is a tool used in political sphere. The forced conversion happened when the Arab armies took the Khzarian capital Saray and forcefully converted their khans to Islam. However, when they retreated, their conversion went along with them. The other happened before the battle of Talas. The Middle Asia was gradually occupied by the Arabs where was mostly Turkish populated area. The Arab-oriented policies (I am trying to avoid anachronich terms) of Ummayad Caliphate, like forceful conversions of infidels, even converts were treated as second class citizens etc. and during the Abbasid period, the policy of raising an army of slaves who were preferably Turks because of their military skills can be classified as forced conversion. When more mild policy of Abbasids settled, conversion in Islam became advantageous for those under their rule because of excemption of certain taxes. But they were not still resulted as mass conversion. The first Muslim convert in Middle Aisa is regarded as khan of Kara-khanids, Satuk Bughra Khan. After him and conversion of chiefs of clans, Turks become Muslim step by step. BUT, there is a very important point in this long period, the Turks learned Islam from Persians. Even today, many words relating the religious practices of Islam like namaz=five times pray/salah in Arabic, abdest=ritual washing before the salah were Persian in origin. Mysticism in Islam transfered from them to the Turks. Thus, there was a strong Persian religious influence on Turks during the conversion. Forgot to mention: Some claims that there were very important similarities between Islam and Tengrism which was Turks' shamistic religion and encouraged them for conversion. But it is not too convincing and seems that it is an attempt to make the process more peacefully. I would like to recommend some books and articles on it, but many of them are in Turkish language. A well known Turkologist Claude Cahen wrote about a book on this issiue if you want. Sorry for bad English by the way, it is not my native language.

Just to clarify for someone who could answer this, do you mean the Turkish (i.e. Ottomans and modern day Turkey), or do you mean the Turkic tribes in general (they span across a vast amount of Asia)?