Approaching non-Muslims has to be in a courteous and delicate way; firstly to attract them and secondly to set a good example for Muslims. Moreover, the one who intends to argue with them has to be well-knowledgeable, otherwise he will fail in convincing them and will give a distorted image about Islam.
Speaking on this issue, Dr. Main Khalid Al-Qudah said:
The best way to approach non-Muslims is to call them to the oneness of Allah (Exalted be He) and disclaim polytheism, and not to have partners with Him.
Allah Almighty says: (Say: O People of the Scripture!, Jews and Christians, come now to a word agreed upon between us and you, and it is, that we worship none but God and that we do not associate anything with Him, and do not take each other for lords, beside God and if they turn their backs, in rejection of God’s Oneness, say, you to them: ‘Bear witness that we have submitted?) (Al `Imran 3: 64)
Also, when the Prophet (peace and blessings be upon him) sent Mu`adh bin Jabal to Yemen, he advised him saying: You will approach the people of the Scriptures, and that the first thing to start with is to call them to believe in the oneness of Allah, and that Muhammad is His servant and His Prophet.
As of the infidels (those who do not attribute themselves to any of the Divine Religions) and atheists (those who deny the existence of God); introducing Allah to them as the only creator, maintainer, and sustainer of the whole universe is the best approach. This could be done by emphasizing the perfection of creating the heavens and the earth, the variety in all creatures, the diversity of human beings, etc. Once they recognize His ultimate power and the perfection of His creation, the next step is to call them for worshipping Him alone because He is the only One worthy of worship because of the aforementioned facts. A part of that is to believe in all the prophets and messengers He sent to guide humanity to the right path, including Muhammad (peace and blessings be upon him).
In case the above did not work out, especially with the people of the Scriptures because they follow what is written in their Scriptures, then arguing with them in a good way is the second step. Almighty Allah says: (And do not argue with the People of the Scripture but in the most virtuous way, except f
or the aggressive people amongst them, and say; we believe in what has been revealed to us and revealed to you. Our God and your God is the same, and to Him we submit?) (Al-`Ankabut 29:46)
Argument should focus on discussing the authenticity of the current Scriptures they already have because of the long period of time between the revelation of these Scriptures and the beginning of their documentation, consequently, questioning the genuineness of what is written therein.
In addition, the fact that current Christians have more than one Bible, although what was reveled to Jesus (peace and blessings be upon him) was only one Bible, should be highlighted. The original language of the Scriptures was not Arabic or English. So, the possibility of changing the meaning is highly expected, leave a side the accuracy of the translation itself.
It may be good to refer to the great effort of Sheikh Ahmad Dedat (may Allah have mercy on his soul) in this field. Another expert in interfaith dialogue and comparative Religions studies is Dr. Jamal Badawi, may Allah bless them and their effort.