When witnessing, I've found, that living the holy life Christ called us to is 1st.
Loving God 1st and expressing Love, care, and concern to others 2nd.
If you don't have those as ur foundation, then give up witnessing NOW.
But if you have that down. Find out WHY they believe what they believe. Ask them "why don't you go to church?" 'what is your background with any church denomination?" "what are you views about Christ?"
Find out what they believe and CARE for them. Don't just downcast their beliefs. Jesus NEVER did that to an unbeliever. He 'downcasted' the proud religious people of his day.
If it's 'answers' they want. Ask them 'how many answers is it going to take'. *(The bible says the Gentiles seek after an unquenchable wisdom and Jews after supernatural signs; they both are unable to fill. [1 Cor. 1:22] It's ONLY the Spirit of God who can convert a soul.[John 16:8])*
If they seek a 'sign'. Share with them the Word of God.
Honestly. All that I said could be meaningless. Why? Because God might be leading you otherwise to say something else to person. Follow GOD's Leading not mine.
But, I believe this is very biblical "If your not aiming on keeping the greatest 2 commandments then give up evangelism."