Our goal is the help you understand what muslims believe to help you to witness to muslims. When I am witnessing to muslims I witness to them the same way that I witness to others except that I go over justice first.
If I know right away that a person is muslim I will poss the following sinerio first. If a person raped and murdered your best friend. When the murder stood before the judge if the judge would say that is ok I am merciful and I will just let you go would the judge be a good judge? They will say no. Should the judge punish the person? This sets up that only a corrupt judge would let the person go.
Next I take the person through the good person test. I ask them if they would consider themselves a good person? I ask them if they have kept the law of Moses? Have you ever told a lie? Have you ever stolen anything? Jesus said if you hate someone you have murdered them in your heart and if you lust after a person you have commited adultery in your heart. If God judged you by the law of Moses would you be innocent or guilty? Would you go to heaven or hell? Remind them that if God is a good God then he must punish those that break his law or he is wicked. You need to go through and show them that it only makes sence that God would be just. Then you can explain that Jesus can be merciful because he died on the cross and paid their fine so he can be just and merciful. This understanding is very important.
Other issues that you need to explain to muslims is how there can be 3 persons in 1 God. I explain that God is like a band. All the members of the band can sing and are able to play all the instruments but each has a role that they play. They are all important but there is order. God the Father is the head. Jesus obeys God the Father and the Holy Spirit obeys God the Father and Jesus. The Christian household has this same order. The husband it the head of the household. The wife obeys the husband. The kids obey the father and the mother.
Often times you have to explain the many versions of the Bible. Here is the basic answer: The Bible versions are all translated from the same origials. They are just translated into a version that you can understand and different reading levels. Some are a word by word translation and some are a concept translation.
You can spent time if you like going over the issues with the Koran.
If Allah is God then he should know what other religions believe. Would you agree with that? In the Koran it sayes that Christians believe the trinity is Father, Son and Mary. Show them that the Koran gets that incorrect. This maybe a hard direction to go however. You want to take them to Surah 5 to see this. I am not going to quote it because you will want to read this and learn to make your own argument.
It is also a good idea to read up on what they believe. The Carm.org site is great for learning about Islam.
Below are video's about what Islam teaches.