The fool says in his heart, “There is no God.” (Psalm 14:1)
This is the objection of the person convinced by the world that there is no God. Most often, the individual has not seen the evidence, nor has this decision been made as a purely intellectual one. Typically, a person denies God because they don’t want the consequences of belief in God, namely, ethical behavior. They want to do whatever they want without a God looking over their shoulder. Arguing the existence of God will not change his position. They will continue to cite “evidence” of “Scientists” and say that anything religious is just begging to be believed.
Always begin your responses with Prayer, so that God will help you with the words. Remember that an atheist is one who has been personally hurt by the Church or by the choices they believe God has made against them (i.e., He didn’t cure my saintly mother from cancer). So you must deal gently, not with an argument for the head, but listening for the pain in their heart. Atheism is rarely purely intellectual, nor can it be son soley with logic.
You might ask the person if they know absolutely that there is no God. Ecclesiastes 3:11 says that God has set eternity in the hearts of men. Every man knows there is someone beyond his understanding. God put it there. The typical “atheist” is actually a hurt agnostic. He will admit that he doesn’t know “absolutely” that there is no God. He will cite evidence from evolution, or say that evil exists in the world, or something equally dismissive. (These arguments he has developed as walls for his conscience to reassure himself that it’s ok to be an atheist because God can be reasonably doubted.)
If he uses the argument of evil, remember that we would not know what evil is without knowing what is good. The fact that good exists, and that a standard of good and evil exists, points to greater moral sense among all cultures, and introduces what C. S. Lewis calls the Moral Argument for God’s existence. God put this morality into all people, because He is the Moral Lawgiver. (Romans 2:14)
Repeat back to him his own statement positively, “so you think there might be a God? And if there is a God, how would you know it?” He would probably ask for some miracle or evidence of supernatural things. Then you can talk about God’s word – the Bible as a written revelation of God to Man or God’s Son – the personal revelation of God to Man, or just about the miracle of the resurrection, attested to by many ancient witnesses. What you’ve done is cause doubt in his own presumptions, perhaps enough doubt for him to peek over the wall of his arguments and see God for who He is. This may require repeated discussion, and certainly love and patience, but you will have an opening into this man’s life for future conversation and conversion. You may offer to pray with him before you are done talking to him.
P.S. Since this post has generated a bit of attention via comments, I am going to add an additional free resource (well, I got it free anyway) that I have that I want to pass on. This is a PDF of a brochure that addresses many of the common rebuttals listed both above and in comments.