Also, by following their arguments, trying to clarify it and understanding the pieces. Your sincere and genuine attempt to understand them in the best possible light will make them open to your point of view.
The smart Christians are some of the most logical people I’ve ever met. There worldview fits together like a kind of Geometry. They know that you get a completely different form of it if you substitute one axiom for another (existence of God for non-existence of God), much like Euclid’s world dissolves without the parallel postulate.
Once we got to that point in our conversation, I realized that they we agreed on everything about the world except that postulate, which they were also aware of. I realized that they were neither stupid nor evil, as I had assumed before (a remarkably common, and uncivil, view that atheists have of believers). I still disagree with them. However, I was fine with leaving the conversation with both of our positions unchanged, but understanding each other better.
I am curious about the large emphasis that rationalists place on the religious belief. Religion is an old institution, ingrained in culture and valuable for aesthetic and social reasons. To convince a believer to leave his religion, you need not only convince him, but convince him so thoroughly as to drive him to take a substantial drop in personal utility to come to your side (to be more exact, he must weigh the utility gained from believing the truth to outweigh the material, social, and psychic benefits that he gets from religion).
For rationalists’ attention, there are myriad more important and relevant issues where human irrationality has an effect on the world. In addition, these issues are normally easier to change people’s beliefs about.
People have been believing in God for 500,000 years. People have been believing unsupported things about Global Warming for 30. I would rather teach people how to be skeptical and cautious about modern policy debates than have Yet Another God Conversation.
I was scarred by religion growing up. I understand the impulse to despise it and oppose it. But there came a time in my life when I realized that it was going to be around for as long as humanity, though its fortunes may wax and wane. It’s time to move on.