To find common ground, we must stay focused on the concept of truth. Knowing the truth is something upon which every rational person places a premium. Apart from needing truth to stay alive (eg. is it true that poison can kill me? Is it true that looking into the sun will blind me?), it is apparent that no one wants to be deceived. No matter how accomplished a liar someone might be, they never want to be on the receiving end of the lie. This shared interest in truth can be the starting point of a productive conversation.
I would begin with an observation. If the atheist is correct, doesn't the centrality of truth seem rather odd? If what we see around us is the random product of chance, then whatever feels good or whatever works should prevail, regardless of the underlying truth of the matter. But that isn't how people actually behave; though they desire good feeling, they also care, intrinsically, about knowing the truth. I would also note that not all truth claims are of equal importance. Is it true that my favorite sports team lost last weekend is not as important a question as whether it is true that John Smith, and not his twin Joe, was the shooter in a homicide case. Or that the syringe contains insulin and not arsenic.
If, then, there is such a thing as truth that we intrinsically seek, and if some truth claims are more important than others, then it follows there must be an ultimate truth claim, an issue beyond which no greater issue can be imagined.
That ultimate truth claim, I would submit, is what happens after you die. Is God really there? Does he have a plan, not for his whole creation, but for you particularly? In other words, is this present existence all there is, or is something more in store for you? And if there is, what is expected of you?
The skeptic may respond that some people actually do not want to know the truth, that the truth really isn’t as important as I am suggesting. Isn't it the case that many people run or hide from the truth? Perhaps a person refuses to go to the doctor because he is afraid of what the diagnosis might be. Or a spouse refuses to acknowledge evidence of infidelity. This, of course, does happen, but it bears noting that even in these situations, the truth actually matters to the person; they are simply afraid to confront or acknowledge it. It also bears noting that running from the truth doesn't help in the long run. It may forestall the day of reckoning, but even in these examples of people hiding from the truth, it is apparent that one cannot hide forever. The underlying truth does not change because they refuse to acknowledge it.
The skeptic will also say that these are but “scare tactics” - the believer is trying to scare atheists with the specter of the God of wrath, and being enlightened people, they won’t believe in such a God. But the threat of punishment - of separation from God - is merely the flip side of the coin; it cannot be separated from the notion that what really matters is not whether God is harsh for punishing us, but rather whether he has something wonderful in store for those who follow him. This is no different than parents who urge their children to study hard and be productive so that they can have interesting careers and fulfilling lives. They concentrate on the positives that come from right behavior, even though they are intrinsically aware that there is always another side to that coin, the possibility of hardship and poverty for those who refuse to prepare and plan for tomorrow. It’s not a scare tactic to let people know the truth; an appreciation of both the pros and cons of our choices is a matter of great importance. It is no different when the discussion is about ultimate things.
Many skeptics think there might be a God, but they don't want to be afraid of him. On the other hand, they don't want to spend any time thinking carefully about whether Christian truth claims are in fact true. But if they are true claims, they don't go away simply because someone does not want to acknowledge them. And the issue isn't really what punishment will be meted out. In the end, the issue is what you might miss out on, in terms of ultimate fulfillment, and ultimate happiness, if you wait too long to consider the question.
The bottom is line is truth. I believe in Jesus because I believe it is true that he is who he said he is and that he died and rose again as he said he would do. This makes him quite unique in the history of the world, and worth learning about it. And because these things are true, we can place our trust - and our destiny - in him.