Islam Ottoman Empire had originated in the early 14th Century in Anatolia. But then Islam was present in Anatolia long before the Empire had emerged. But then if you take the time between the 14th and 16th Century then you will find that Islam had spread due to the conquests of the Ottoman in central Hungary and also the Balkan Peninsula. But then this does not necessarily mean that the entire population was Muslim uniformly.
In many parts of the Ottoman Empire it wasn't an Islam Ottoman Empire. Take for example the Balkan region where the bulk of the population was Christians. Even in areas where you would find mostly Muslims there were other non Muslim citizens as well. The Ottoman Empire Sultans had never tried to convert their inhabitants; they had never really imposed a Muslim uniformity either. But then the dominant religion in this Empire was undoubtedly Islam.
You could see this in the political structure of Islam Ottoman Empire. The entire dynasty was Muslim, till the 19th Century reforms any non Muslim wasn't allowed to hold a post in a military command or political office. The Christians and Jews were only allowed to take part in the maintenance of the entire Empire by paying taxes, being farmers and so on.
When the Ottoman Empire had emerged in the 14th Century, Islam had turned out to be a fully fledged form of belief along with various intellectual, cultural and legal attributers. Knowledge was the main concept or what we can call knowledge of God through the help of revelation. According to the religion, God reveals himself through the help of various prophets.
Islam Ottoman Empire made sure that there was the study of this religion in the form of sacred texts, sciences and so on. They would study various interpretations of the Koran, theology, law, hadith and also dogma. Through these sciences it was believed that one could get god and this basically comprised of the central Ottoman curriculum.
Tasawwuf was a strong influence on the beliefs of Islam Ottoman Empire Muslims and this could be seen in its literature, music and also its visual art. But then there are various literary fragments from that era which suggests that Islamic learning during the 14th Century was quite low. Before people would travel to Cairo or Damascus in search of learning Islam but then after the 15th Century, colleges were built and it could be learnt in the Empire itself.