I always give Christians two pieces of advice if they want to talk Muslims. First, focus your message on what really matters: the Gospel. After all, we’re commanded to tell people about the message of reconciliation as ambassadors for Christ (2 Cor. 5:18–20). Muslims believe Jesus is a prophet and was given the Gospel as a revelation. So, they’ll be somewhat open to talking about Jesus and His message.
Second, avoid conversations that distract from the Gospel and/or create a defensive posture. For example, bringing up violent jihad, making denigrating comments about Mohammed, or debating the Israeli-Palestinian conflict typically raise defenses and distract from the main message that God wants them to hear: His offer to them to be reconciled to Him. I’ve found it much harder to get back to the Gospel once the conversation has moved to topics that put the Muslim on the defensive.
As Greg Koukl has said, “The Gospel is offensive enough. Don’t add any more offense to it.”