Sura 29 ayet 46

And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims (in submission) to Him."

I think that is one of answers

Also about behavior of a muslim towards a non-muslim
How did Muhammad (pbuh) was tolerant you can read at book The Life of the Prophet Muhammad (Peace and blessings of Allah be upon him) part about Treaty of Hudaybiyah

Soon after this, official 
messengers came from Quraysh and talks began for a peaceful settlement. 
A man called Suhayl ibn 'Amr was sent by the Meccans to work out a 
treaty. When the Prophet (pbuh) asked 'Ali to write 'In the Name of Allah, 
the Most Gracious, the Most Merciful', on the top of the page, Suhayl 
objected, saying 'Write only: bismik Allahumma (in Thy name, 0 Allah). 
I don't know him as al-Rahman (the Most Gracious), al-Rahim (the most 
Merciful).' The Prophet (pbuh) agreed and dictated: 'This is a treaty 
between Muhammad the Messenger of Allah and Suhayl ibn 'Amr.''Stop!' 
cried Suhayl, 'I don't believe that you are Rasulallah (the Messenger of 
Allah). If I thought you were Allah's Messenger, I wouldn't be fighting 
against you, would I?' Calmly, the Prophet (pbuh) agreed that he should 
be referred to in the treaty as Muhammad', son of 'Abd Allah. The 
Muslims were very upset at this, and 'Umar furiously cried out, 'Are you 
not Allah's Messenger, and are we not Muslims? How can we accept such 
treatment when we are right and they are wrong? This will make people 
laugh at our religion!' But the Prophet (pbuh) knew what was best and the 
Treaty of Hudaybiyah was signed.  

Surah 29 ayah 46

And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims (in submission) to Him."

Also regarding the behavior of a Muslim towards a Non-Muslim,

How Muhammad (pbuh) was tolerant: you can read in the book The Life of the Prophet Muhammad (Peace and blessings of Allah be upon him)

Here is a part about the Treaty of Hudaybiyah

Soon after this, official 
messengers came from Quraysh and talks began for a peaceful settlement. 
A man called Suhayl ibn 'Amr was sent by the Meccans to work out a 
treaty. When the Prophet (pbuh) asked 'Ali to write 'In the Name of Allah, 
the Most Gracious, the Most Merciful', on the top of the page, Suhayl 
objected, saying 'Write only: bismik Allahumma (in Thy name, 0 Allah). 
I don't know him as al-Rahman (the Most Gracious), al-Rahim (the most 
Merciful).' The Prophet (pbuh) agreed and dictated: 'This is a treaty 
between Muhammad the Messenger of Allah and Suhayl ibn 'Amr.''Stop!' 
cried Suhayl, 'I don't believe that you are Rasulallah (the Messenger of 
Allah). If I thought you were Allah's Messenger, I wouldn't be fighting 
against you, would I?' Calmly, the Prophet (pbuh) agreed that he should 
be referred to in the treaty as Muhammad', son of 'Abd Allah. The 
Muslims were very upset at this, and 'Umar furiously cried out, 'Are you 
not Allah's Messenger, and are we not Muslims? How can we accept such 
treatment when we are right and they are wrong? This will make people 
laugh at our religion!' But the Prophet (pbuh) knew what was best and the 
Treaty of Hudaybiyah was signed.  

Sura 29 ayet 46

And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims (in submission) to Him."

I think that is one of answers

Sura 29 ayet 46

And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims (in submission) to Him."

I think that is one of answers

Also about behavior of a muslim towards a non-muslim
How did Muhammad (pbuh) was tolerant you can read at book The Life of the Prophet Muhammad (Peace and blessings of Allah be upon him) part about Treaty of Hudaybiyah

Soon after this, official 
messengers came from Quraysh and talks began for a peaceful settlement. 
A man called Suhayl ibn 'Amr was sent by the Meccans to work out a 
treaty. When the Prophet (pbuh) asked 'Ali to write 'In the Name of Allah, 
the Most Gracious, the Most Merciful', on the top of the page, Suhayl 
objected, saying 'Write only: bismik Allahumma (in Thy name, 0 Allah). 
I don't know him as al-Rahman (the Most Gracious), al-Rahim (the most 
Merciful).' The Prophet (pbuh) agreed and dictated: 'This is a treaty 
between Muhammad the Messenger of Allah and Suhayl ibn 'Amr.''Stop!' 
cried Suhayl, 'I don't believe that you are Rasulallah (the Messenger of 
Allah). If I thought you were Allah's Messenger, I wouldn't be fighting 
against you, would I?' Calmly, the Prophet (pbuh) agreed that he should 
be referred to in the treaty as Muhammad', son of 'Abd Allah. The 
Muslims were very upset at this, and 'Umar furiously cried out, 'Are you 
not Allah's Messenger, and are we not Muslims? How can we accept such 
treatment when we are right and they are wrong? This will make people 
laugh at our religion!' But the Prophet (pbuh) knew what was best and the 
Treaty of Hudaybiyah was signed.