There are endless reasons for choosing atheism, but I have found that atheists fall into three major categories: the intellectual atheists, the offended atheists and the cultural atheists.
One simple way to strike up a conversation is to simply ask “So what do you think about spiritual stuff?” This can be done during a conversation that involves death or spirituality. If the person responds “I’m an atheist,” you can ask, “So why don’t you believe in God?” That will usually give you an indicator as to what type of atheist they are and whether or not they are interested in continuing the conversation.
The intellectual atheist
These folks usually come off as confident and informed about why they don’t believe. They often view Christians as uniformed and unintelligent. These types of atheists often picked up their unbelief in university. But the truth is, they are usually misinformed. With this group it is important to have good questions, good answers and be very gracious.
John Lennox has done a great job of this in his debates with Richard Dawkins. I recommend watching one of their debates to see how Lennox does this. You can view one at https://vimeo.com/130616490 There are a lot of great resources to help you get informed. One book I suggest is Why I am a Christian available for $11.99 at http://shop.gospelfolio.com/Why-I-Am-A-Christian-Leading-Thinkers-Explain-Why-They-Believe/productinfo/X-2104/
The offended atheist
When asked why they don’t believe in God, this type of atheist may retort with a variety of reasons, but the emotion in which they respond will be the indicator that there is a deeper reason. This person needs unconditional love, patience and someone who is willing to listen.
Offended atheists are often offended for good reason. I’ve talked to some that have been abused by religious authority figures or seen their children die of horrific diseases. Reasoning with these people often comes off as giving pat answers to their hurt.
After you have shown real compassion and been praying for them, let them know that God cares about their hurt and that the things that hurt them hurt God too. Pointing them to the cross, you can let them know that God understands suffering and betrayal.
The cultural atheist
Cultural atheists have been raised in irreligious environments and have simply accepted the worldview that they were taught. They often view religion as outdated if they think about it at all. They are often uninformed about what they believe.
Asking good questions and presenting the gospel is very important. Ask them why they don’t believe in God and what do they mean when they say things like “I believe in science” or “the Bible is full of contradictions.”
All these groups need love, prayer and good questions. The love will show them that Christians really do care and God cares too. The prayer will be to call God to work on their souls. The questions will encourage them to think about the unbelief they have accepted, which they often try not to think about (Romans 1:18).