Jesus was confronted by people called the Sadducees, who "say that there is neither resurrection nor angel nor spirit.." Acts 23:8
They kept asking Jesus questions that were designed to show that what he was teaching was false, and what they taught was true. Jesus was able to answer all of their tricky questions with a clear knowledge of the scriptures and sound reasoning. Jesus is our example.
Jehovah's witnesses have a sound and comprehensive program of Bible study that is freely available to anyone who is willing to take the time. We have meetings that take us through the scriptures chapter by chapter, opportunities hear Bible research as presented to the congregation and by congregation participants, and our Awake! magazine has featured dozens of articles on science and evolution. In recent years, the Watchtower has also featured many articles on atheism. So when we get to speak to atheists in our ministry, or in day to day life, we do not need to be nervous about talking to them, when they are willing to talk to us.
We do not think that we have the right to try to make a person believe things. People have to make up their own mind. But if they are willing to talk, we will offer them something to think about. We can offer them what God has provided as evidence of his existence, and then they have to decide what to do about it.
For instance there was an article called "The 20th Century Denial of God" which made this statement:
Some, however, feel that it is illogical to believe in God, since we cannot see him. But what about air, sound waves, and odors? We cannot see any of these things, yet we know they exist. Our lungs, ears, and noses tell us so. Surely, we believe in what cannot be seen if we have evidence.
After contemplating the physical evidence—including electrons, protons, atoms, amino acids, and the complex brain—natural scientist Irving William Knobloch was moved to say: “I believe in God because to me His Divine existence is the only logical explanation for things as they are.” (Compare Psalm 104:24.) Similarly, physiologist Marlin Books Kreider states: “Both as an ordinary human being, and also as a man devoting his life to scientific study and research, I have no doubt at all about the existence of God.”
These men are not alone. According to physics professor Henry Margenau, “if you take the top-notch scientists, you find very few atheists among them.” Neither the advances of science nor the failure of religion need force us to abandon belief in a Creator.
But the Bible has an historical basis that is far beyond mythology, the cities Jesus Christ walked in are still in existence today. Can you explain that? Many tribes are still available today that the bible speaks of, Hebrew is still being spoken today. These are all real aspects of the Bible, the only book that's been translated in almost all languages and has a history behind it. The fact that there are real elements in the Bible, ever wondered why people call themselves certain names? Can be traced back to biblical origins.
So the only way to approach atheism and atheists is the same way that Jesus did: honestly, sincerely, and by becoming clearly familiar with the inspired scriptures and how they answer the questions presented by atheists and others who question the truth about God, and, by preaching the good news of the kingdom of God without letup. Matthew 24:14, Luke 8:1