This is a really big topic and I'm on my phone right now, but I'll try to do it justice.

The first thing to remember is that the Ottomans generally didn't care what faith you were (unless you were Shia, in which case you'd face random punitive actions from the central government). The Ottomans set up religious courts (millets) for non-Muslims and frequently allowed a degree of self-rule in frontier provinces (many of which were vassals before being absorbed).

Religious conversion was carried out in the local level. Being Muslim was often a way to open doors to higher government posts. This was sometimes literal: only Muslims could enter the Dome of the Rock, for instance. And sometimes it just made things easier, especially for merchants involved in silk or spice trade. And, of course, state-sponsored dervish lodges did a fair bit of "outreach" to minorities. This is the main contributing factor to the spread of Islam in Albania.

The only notable exception to the above, at least until the later years, was the devsirme. Those taken by the devsirme would essentially be indoctrinated into Islam and, when they retired, they took their new faith with them. Sometimes these retirees would return home and sometimes they'd receive a town or something to govern (the father of the Barbarossa pirates was given a town on the island of Lesbos, possibly for heroism, though records conflict).