How is the proof established against non-Muslims?

There are several ways to invite non-Muslims to Islam: these include good treatment and noble character, and gifting books that introduce Islam. They can also be invited through verbal communication regarding simple matters such as the fundamentals of faith, obligatory duties, and noble morals, which are suitable for their common folk. As for debating scholars of other religions, this requires extensive knowledge and firmness in belief, in order to refute their misconceptions. This is specific to scholars and students of knowledge. The invitation must be based on insight, by first understanding the correct creed, and then understanding the beliefs of those being addressed and how to refute them, through books by knowledgeable scholars specialized in refuting them, such as "Al-Jawab Al-Sahih li man Baddala Din Al-Masih" by Ibn Taymiyyah and "Hidayat al-Hayara" by Ibn al-Qayyim. Allah Almighty has gathered the methods of دعوت in His saying: "Invite to the way of your Lord with wisdom and good counsel, and argue with them in the best way."