I want to know how to exactly preach Islam to non-Muslims properly. Ive seen non-Muslims say that "pushing religion on me puts me off religion" and stuff like that. What should we do and how? Are there any hadiths or Quran verses about how?
One hadith is sufficient to force men/women of understanding to search about the true religion.
O Allah, I seek refuge in You lest I misguide others, or I am misguided by others, lest I cause others to err or I am caused to err, lest I abuse others or be abused, and lest I behave foolishly or meet with the foolishness of others.
Abu Dawud, Ibn Majah, An-Nasa’i, At-Tirmithi. See also Al-Albani, Sahih At-Tirmithi 3/152 and Sahih Ibn Majah 2/336
I have never seen a sincere prayer or intention than this in my whole life.
Secondly verse of mubahala is also good to challenge rebellious people if they believe in an almighty