1. Establish rapport with small talk.
2. Ask them about their hope before Allah. They will likely talk about doing the daily prayers and maintaining the five pillars of Islam.
3. Ask them if they are sure if Allah will accept them. Most likely they will not be able to give a full affirmative.
4. It is good to show some knowledge of Islam, including references to the Qu'ran and possibly some a-Hadith. Examples:
a. Surah 4:157 - the Qu'ran denies the Jesus was crucified, but that "it was made to appear" that way. Most orthodox Sunni Muslims believe Judas or Simon the Cyrene was crucified in the place of Jesus by mistake. Ahmedi Muslims believe that Jesus was crucified, but did die (swoon theory). If Allah's intention was that people were misled about Jesus dying by crucifixion, then He started Christianity by mistake. Ironically, only Muslims and radically skeptical atheists have any reason to believe that the historical Jesus of Nazareth died by crucifixion.
b. Surah 5:46-47 - the Qu'ran says that Jesus confirmed what was in the Torah by the Gospel that was given to him. The Qu'ran then instructs the people of the Gospel (Christians) to judge by what Allah says in the Gospel. Basically, when we obey that command, we find that Mohammed contradicts it and he did not really know what was in the Gospel.
c. Surah 4:171; 5:17; 5:72-75 and others deny the deity of Jesus, but seem to misunderstand the Christian teaching of the Trinity. It claims that Christians associate other "partners" or "gods" with Allah and even hints that Mohammed thought that the Trinity was Allah, Mary, and Jesus. If the Qu'ran is from Allah, He should have known what the Christian doctrine of the Trinity really was.
5. Know the story in the Hadith (Sahih Bukhari Volume 4, Book 56, Number 676) of the man who killed 99 people and how Allah saved him. With some Hadith stories, people receive a lot of mercy and get into paradise. With other Hadith stories, there are those who are faithful and they do not make it.
6. Explain the basis of forgiveness from God. In Islam, the forgiveness and punishment from Allah seems arbitrary. In Christianity all sin is punished (either in Christ or in the sinner without Christ). In Christianity, we have a perfect mediator through the God Man and His atonement on the Cross. In Islam, you have no mediator and no assurance.
Hope this helps.
Thank you brother. This has been the best advice on this thread and I appreciate it. Since I do not know any Muslims and they seem to be rare in DT Denver on the streets I had the thought of sending a letter to a Muslim place of worship. I have some books on the Muslim faith, and I believe some tracts as well (http://www.fellowshiptractleague.org/tract_html/english/160/page_flip/160.html) but what are the odds they will respond? I will write my letter in gentleness and respect (1 Pt 3:15) and pray for a response. I have prayed over all my letters I have sent out and shall pray for an opportunity to witness to a Muslim.
John