Here’s an article at Reasons for God that explains a few simple questions that you can ask your atheist friends.

He writes:

Though it has been persistently marketed to us as a worldview that stands for reason and science, the truth is that the atheistic worldview is riddled with contradictions and outlandish claims. And because most secular people haven’t studied why atheism is true, an excellent evangelistic strategy for you and your church is to understand these five challenges for atheism.

In my experience, it is only once people realize that their own worldview doesn’t work that they become interested in seeking something that does. While some would suggest you just have to wait for people to hit rock bottom, I think a more gracious and effective approach is to humbly challenge their pretense to have a sensible worldview.

By God’s grace, studying these five holes in the atheistic worldview can create a powerful opportunity for you and your church to share the wisdom and love of Jesus Christ.

[…]Because of their fundamental commitment to impersonal matter and laws, the atheist faces very difficult problems in at least five unique areas:

• Consciousness
• Free will
• Purpose
• Reason, including mathematics and science
• Objective moral facts, including universal human rights and the reality of evil

Here’s my favorite of the 5:

Leading atheists such as Sam Harris dismiss free will as a matter of course. Or as Tom Clark at Naturalism.org puts it, “Judged from a scientific and logical perspective, the belief that we stand outside the causal web in any respect is an absurdity, the height of human egoism and exceptionalism.”

Dr. Angus Menuge, the current President of the Evangelical Philosophical Society, explains the problem: “before we can talk of being responsible for our decisions, we need an account of why those decisions belong to us. But the trouble is, on a naturalistic view, there is no entity that can plausibly own any mental states, there is simply a plurality of parallel, impersonal processes in the brain.”

The denial of free will logically leads to the denial of personal responsibility for any of our behaviors or beliefs. But if everything about “you” is determined, then “you” could not have reasonably chosen to believe what you do. If a-rational things and laws determined your neurological structure, “you” literally cannot make any decisions about what you believe or why you believe it.

This article is worth a look if you want to start a discussion with an atheist.