From what I know from speaking with those who have been missionaries in Islamic countries and from reading books written by such people, it seems that the strategy is not to demonstrate that Islam is incorrect, but to simply present Jesus (the prophet Isa) to people. Jesus is acknowledged as a prophet by Islam.
The Koran on Jesus
The Koran talks about Jesus and says quite a few good things about him. I actually met a man who was formerly a Muslim from a very Islamic country who discovered for himself from the Koran that Moses received the Law, Mohammed received the Koran, but Jesus received the Spirit. He reasoned that what Jesus received was greater than the Law or the Koran, and so he went in search of Jesus. So, pointing Muslims to the verses in the Koran about Jesus is one strategy that is used.
The Koran on the Word of God
Another tactic is to read the verses in the Koran that teach how God's word cannot be changed and its commands to read the Scriptures given beforehand. Many Muslims are taught that the Bible is corrupted, but the Koran contradicts this by saying that God's word cannot be altered. This often leads Muslims to start reading the Bible.
Finally, it seems that quite a few Muslims have had dreams where Jesus appears to them. So common is this that some missionaries have simply started to ask Muslims that they meet if they have ever had a dream about Jesus.
So, again, the strategy with followers of Islam is pretty much the same with anyone else. Jesus is presented as the eternal Son of God, crucified, and risen from the dead. The point is not to criticize other teachings, but to exalt the Lord Jesus Christ.