How do Muslims proselytize* in non-Muslim areas?

*First off, I realize that in many Mulsim countries proselytize is contentious term. In many Muslim countries, for example, it is illegal for Christians to "proselytize," by which it is believed that non-Muslims are using incentives in order to convince Muslims to drop their faith. I considered using the term "Evangelize," but the root of that word is a specifically Christian word to mean "to announce the Good News." Finally, I considered asking "How does Islamic Missiology work?" but that too seemed a loaded term. So, here's how I would describe what I am looking for - Islam is clearly a growing religion. That implies that there exists a cadre of Muslims who would seek convince non-Muslims that they should become Muslims. I would suspect that like other religions, including Christianity, that means that some even feel compelled to leave the lands of their birth in order to promulgate the religion. From earlier questions, I have gathered that convincing one to become a Muslim does not necessarily entail suggesting to others that they read the Quran and then choose to follow its theology. From what I have gathered here, there seems to be a very deep level of traditional practices that are undertaken once one has become a Mulsim, but what I am trying to understand is the path by which a non-Muslim is enticed or mentored to start down that path in the first place. Again, in Christianity, for example, a person who feels called of God to become a missionary will typically leave for distant land, form relationships with locals, and then in the course of that relationship, typically suggest that the Bible addresses the problem of sin in one's life. The concept of grace - namely that God forgives sin - is shown through the Bible, and if a person chooses to be forgiven of their sin, they are often then invited to become a Christian in order to learn how to live in the context of that freedom. - The method of evangelism would then be relationship driven. - The "What's in it For Me?" would be forgiveness - The first step would be to encourage the would-be convert to read the Bible. - The ultimate goal would be to get the convert to make a decision to continue learning about this forgiveness and grace from Jesus, typically in some kind of fellowship. In contrast, my naive understanding of Islam seems to be that it is a highly cultural thing - that one is born into a Muslim culture, and one is expected to simply continue to follow the traditions of the culture. While within the culture a life-long learning of the Quran is praised and encouraged, that would presuppose being born into that culture. If, however, it were merely a cultural thing, then it would not be growing beyond immigration. Within America's prison system in particular, this is demonstrably false. And, since Islam is, in fact, growing, there must be a mechanism by which non-Muslims are enticed into it. I would like to know how that occurs. So the question, again, is, how does a Muslim go about bringing a non-Muslim into the ummah? What techniques, incentives, and methodologies are common for proselytizing amongst those who were not already born into the culture?