The best way to witness to a Muslim is to give them good theology on the following subjects.

• How did Jesus come about.  You have to explain to Muslims that Jesus always existed.  He just took on flesh and was born of a virgin and that he always existed.  There was no sex between God and Mary.  The Holy Spirit put Jesus in her womb with flesh.  Jesus is truly God and truly man but the man part and the God part are not mixed together.
• Trinity is a major issue for Muslims.  The Quran says that if you say 3 you cannot be forgiven.  You need to tell them that there is 1 God that has 3 persons.  Each of the 3 persons is 100% made up of God essence.  God is made of 3 persons.
• Jesus dying on the cross.  God does not die.  The man part of Jesus died on the cross and the God part of Jesus picked up the man part and rose Him from the grave.  So no God did not die.
• Dual nature of Jesus is important for Muslims to understand that Jesus is the Word of God and always existed.  Jesus is God and took on flesh.  The man part of Jesus is tired, hungry and feels pain.  The man part of Jesus has all the needs of every human.  However the man part of Jesus did not sin because he was born of a virgin and did not have a sin nature.  The man part of Jesus does not know everything that the God part of Jesus knows.  The two natures are not intermingled. 

Quran Verses that say the Bible is the word of God from Quran.com

• Torah –Surah 2:87 “Indeed, We gave Moses the Book and sent after him successive messengers. And We gave Jesus, son of Mary, clear proofs and supported him with the holy spirit.¹ Why is it that every time a messenger comes to you ˹Israelites˺ with something you do not like, you become arrogant, rejecting some and killing others?”
• Psalms—Surah 4:163 “Indeed, We have sent revelation to you ˹O Prophet˺ as We sent revelation to Noah and the prophets after him. We also sent revelation to Abraham, Ishmael, Isaac, Jacob, and his descendants, ˹as well as˺ Jesus, Job,
  Jonah, Aaron, and Solomon. And to David We gave the Psalms.”
• Gospels—Surah 3:3 “He has revealed to you ˹O Prophet˺ the Book in truth, confirming what came before it, as He revealed the Torah and the Gospel”, Surah 57:27 “Then We sent following their footsteps Our messengers and followed [them] with Jesus, the son of Mary, and gave him the Gospel. And We placed in the hearts of those who followed him compassion and mercy and
  monasticism, which they innovated; We did not prescribe it for them except [that they did so] seeking the approval of Allah . But they did not observe it with due observance. So We gave the ones who believed among them their reward, but many of them are defiantly disobedient.” (Sahih International)

God’s Word can’t be altered

• Surah 6:34 “And certainly were messengers denied before you, but they were patient over [the effects of] denial, and they were harmed until Our victory came to them. And none can alter the words of Allah . And there has certainly come to you some information about the [previous] messengers.”  (Sahih International)
• Surah 6:115 “And the word of your Lord has been fulfilled in truth and in justice. None can alter His words, and He is the Hearing, the Knowing.” (Sahih International)
• Surah 10:64 “For them are good tidings in the worldly life and in the Hereafter. No change is there in the words of Allah . That is what is the great attainment.” (Sahih International)

Since no one can change God’s words the Torah, Psalms and gospels are to be believed, since they are unchanged.

Christians should judge based on what is in the gospel

Surah 5:47 “And let the People of the Gospel judge by what Allah has revealed therein. And whoever does  not judge by what Allah has revealed – then it is those who are the defiantly disobedient.”

Quran contradicts the Bible so Quran is not true.

If the Quran was written by God then God would know what Christians believe.

Quran says the trinity includes Mary.

Surah 5:116 “And [beware the Day] when Allah will say, “O Jesus, Son of Mary, did you say to the people, ‘Take me and my mother as deities besides Allah ?'” He will say, “Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen.”

Quran says Christians believe in 3 Gods. Christians believe in 3 persons 1 God.

Surah 4:171 “O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, “Three”; desist – it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs.”

Surah 5:73 They have certainly disbelieved who say, ” Allah is the third of three.” And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.