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There's quite a spectrum here, and it might be helpful to refer to a couple of examples. One with a Muslim, and the other a professing Christian who realizes that she probably isn't.
In the former case, I started out by asking questions about Islam. I think in that situation, it's especially helpful to do that, because at least practicing Muslims are often very defensive in a culture that sees them as all... Paints with one brush as all belonging to Al Qaeda. In that defensive posture, it's helpful to ask people, "Tell me what you believe," even if you think you know. It's helpful to know what they think they believe, and then to start from there, and then to get into the historical questions about Islam and Christianity.
I have found that at least in my conversations with many Muslims, there is less interest. Not always, but often less interest in asking you questions about your faith than in trying to convert you. Well, that's true of a lot of us. Having felt what it's like to be on the other side of that, it's made me more concerned not simply to data dump and to actually listen to what other people are saying about what they believe, and then starting there, because the wonderful thing about Christianity is you can start anywhere. You can start with the Trinity. You can start with the human problem, predicament of sin. You can start with the resurrection of Christ.
With this other person who was a nominal believer, she just didn't understand the gospel at all, and she was a lifelong Christian. With her, it was explaining the meaning of justification. Now, in both conversations, I got to the gospel. I got to the heart of what we believe as Christians, and the resurrection was the doorway in both instances, because Islam doesn't have a historical defense that comes even close to the Christian claim of the resurrection of Jesus Christ. The historical evidence, for instance, for the assumption of the prophet Muhammad, the historical evidence for many of the claims surrounding him in the Hadith, it's not there.
With Christianity, you have so much supporting evidence. The gospels themselves, which have far more integrity than you hear on national news, but actually, in critical biblical scholarship, there is a lot more recognition than there was a generation ago of the authenticity and early dating of the gospels.
Then outside of the gospels themselves. Jewish historians and Roman historians, the people with the most to lose in this claim for Jesus' resurrection, nevertheless attested to his birth, that he lived, that he performed wonders, although the Jewish Rabbis said that it was by Satan that he performed these wonders. That he was buried in Joseph of Arimathea's tomb, that a guard was posted there at the tomb, and that three days later, the tomb was empty.