No matter where you are in the world, some principles are universal when sharing Christ (follow the Spirit’s lead, walk in humility, ask good questions and don’t spend all your time giving answers to questions other people aren’t asking, etc.). But here are a few thoughts specifically on sharing Christ with Muslims.
Build Relationships: Most Islamic cultures are very relational. Even in business meetings, participants often spend ample time discussing family and getting to know one another. Often you don’t earn the right to be heard until you’ve invested time building a relationship. But here’s the catch: building relationships doesn’t work if you only have an ulterior motive (even sharing Christ) in mind. So let your motive simply be to show them the love of Christ, and as you spend time with them the door will open to share the hope that you have. Of course, God can do what he wants and open up a door in your first conversation – so always be prepared and follow the Spirit’s lead.
Start with Agreements instead of Disagreements: It would be easy to start out a conversation talking about the differences between Christianity and Islam, but you’ll find that if you start there either (a) the conversation won’t last very long or (b) the conversation will quickly turn into a debate. Since we don’t want the conversation cut short and we’re not looking for a debate (informal debates tend to be unproductive), it may be a good idea to start by finding common ground. As a Christ follower, you actually have much more in common with a Muslim than you do with an atheist. Of course, there are huge, eternity shaping differences – but it’s often helpful to start with agreements and go from there.
Know the Hot Topics: As you get to know more Muslims and get into spiritual conversations with them, you’ll probably notice that there are several hot topics that trouble Muslims about Christianity. Usual hot topics include: (1) Jesus can’t be the Son of God (to say that God has a son is blasphemy), (2) Jesus didn’t really die on the cross (it was another guy who was made to look like Jesus), and (3) the Trinity (often thought to be Father, Mother, and Son). Since you’re almost guaranteed these topics will surface eventually, do a little study and know how to discuss them.
Pray for Dreams & Visions: It’s still the case that a very large percentage of Muslims become followers of Christ after having dreams either directly about Jesus or pointing them to someone who can tell them about Jesus. Pray that God would do this for your new Muslim friend.
Tell a Story: Many Muslim cultures are oral cultures (even if many people in the culture are literate). Many things have been handed down in Muslim culture through stories, so stories are a great way to introduce them to biblical truths. Because many Muslim cultures are based on honor/shame, a few stories that tend to be particularly effective are the Prodigal Son, the Good Samaritan, and the woman who was bleeding (for women).
There are plenty of good books and resources that can help equip you to share Christ with Muslims (Any-3 and The Camel Method are two that are particularly helpful), but your biggest helps will always be a good foundation in God’s word and a steady reliance on the Spirit. God’s word is still able to make people wise for salvation and His Spirit is still able to open the eyes of the blind and bring death from life for the glory of God.