In order to show what Islam is all about, we need to concentrate on learning the common things between their religion and ours. That's how we can grab their attention then later talk about the good stuff that has been ordained in Islam based on listeners interest. Need to judge the opposite person. Is he/she trying to provoke you by saying bad stuff or a good debater or just trying to while away the time, b'cause he is not going to listen whatever you say. Based on your couple of dialogues decide how to move forward.
We need to be careful, while discussing such things, b'cause this shouldn't lead to an argument but instead always try to justify with live examples and a quote from Quran.
Also be prepared to answer the common questions that are asked on Islam (Example - Who is Mohammed (PBUH), Is Quran the word of Allah, justify?, Hijab, Marriage Law, Halal & Haram, Jihad (False impression) etc etc)