The first thing to note is that Muslims believe in the Old Testament. That makes it easy to relate to them through the 10 commandments. Unfortunately, they see the need for repentance and God's forgiveness but think they can attain it and stand before a Holy God on there own merit through works. So if the Law doesn't make them tremble, you will need some more scripture in your holster. Get them to soundly say that they believe at least Genesis to be true. At that point show them Genesis 17:19-21 where it says:
Then God said, "Yes, but your wife Sarah will bear you a son, and you will call him Isaac. I will establish my covenant with him as an everlasting covenant for his descendants after him. And as for Ishmael, I have heard you: I will surely bless him; I will make him fruitful and will greatly increase his numbers. He will be the father of twelve rulers, and I will make him into a great nation. But my covenant I will establish with Isaac, whom Sarah will bear to you by this time next year."
And Genesis 21:12-13
But God said to him, "Do not be so distressed about the boy and your maidservant. Listen to whatever Sarah tells you, because it is through Isaac that your offspring will be reckoned. I will make the son of the maidservant into a nation also, because he is your offspring."
Why are these important? Because in Matthew chapter 1 and Luke chapter 3 it is clearly shown that Jesus(his fully man side) came from the line of Abraham, Isaac, and Jacob through both Mary and Joseph's side. What that means is that Jesus fulfilled what God said when it was told that through Isaac your offspring will be reckoned.
Now that's all fine and dandy but now you will run into the issue that Muslims believe in Jesus, or Isa in the Kuran, but not who He says He is. They believe He was just a prophet like Moses or Muhammad. Familiarize yourself with scriptures that show Jesus' Deity and places He accepted worship etc. Exodus 3:14 and John 8:58 is a great example of Jesus claiming to be the I Am. Also show them John 8:24. It says, I told you that you would die in your sins; if you do not believe that I am the one I claim to be, you will indeed die in your sins." Reason with them that if Jesus was in fact who He claimed, God in Human flesh, that no other prophet would need to follow Him. Talk to them about how the Old Testament speaks of a New Testament in Jeremiah 31 but the New Testament says the opposite and that we are NOT to add to or take away from it. They may try to tell you that John 14:26 is Jesus predicting Muhammad but it is the Holy Spirit Jesus is referring to which did come as predicted on the day of Pentecost. One other hurdle with Jesus is they don't believe He died and rose again. Muslims say He was just taken by God. Instruct them that there were over 500 witnesses to the Resurrected Christ. The Resurrection is what sets our faith apart. I've gone so far as to let my friend know that he can go to Medina and see Muhammad. Jesus left an empty tomb, defeating death!
Remember that you are just to share the Gospel and that when witnessing to Muslims, you are dealing with people who's faith is not only strong but very, very well versed. We said earlier that Muslim people think that they can stand on there own before God. Let them know that God had always required blood sacrifice throughout the Old Testament(which they believe in) and that Hebrews 9:22 says, In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness. This can lead you into Isaiah 53 and Psalm 22, both of which predict the suffering of Messiah.
I hope this is helpful to you guys. This is all from witnessing to one Muslim friend over a period of several months. You may not know any Muslim people but if you are to run into one who is peaceful and friendly as they claim, you should be equipped. These are the Muslims that this article applies to. If you see a red and white checkered headband and an RPG, you might want to slip the Tract back in your pocket. I wouldn't blame ya, I'd have a fear of man then too. But I've found that a reasonable, friendly conversation can happen between a Muslim and Christian. If you have questions, email me at firstname.lastname@example.org