The biggest divide between Christians and atheists is not their views about God's existence, but their beliefs about His character.
In John Loftus's book, Why I Became an Atheist, he quotes "exbeliever," one of his fellow bloggers, who gives the clearest, most accurate illustration I've seen to describe the mindset of outspoken atheists toward God and Christianity. I'm going to quote it here because I think this is the most important thing to keep in mind about atheists when discussing God with them, but I do forewarn you that it's quite disturbing to hear our great God spoken of in this way:
For a long time, I was an ardent admirer of Dr. John Piper. I remember a sermon of Dr. Piper's in which he described God as a flowing fountain of delight.... But what about those of us who have left the fountain with a horrible taste in our mouths? We came to the fountain and drank as deeply as we could and, for a while, could not get enough of it.... But, then, something happened. The fountain became foul to us.... We opened the Bible and, instead of finding wisdom, we found violence and the justification of immoral acts. We found anti-intellectualism and backward thinking. We found oppression....
We tried to hold on to the fountain, but something had changed. It wasn't the fountain; it was our taste for it. We realized that the fountain wasn't a being; it was a religion. It was just dogma. It is like we had been drinking from it with our eyes closed and noses plugged. Somehow, though, we opened our eyes and unplugged our noses and discovered that we had been enjoying filth. The fountain was a fountain of blood and other foul things. We realized that we had spent most of our lives consuming a vile concoction.... We wanted to help [other Christians] open their eyes and see what we saw.... We described the filth to them, but even when they accepted that the fountain contained blood and other "foul" things, they insisted that those things were really "good" [emphasis mine].
I have a very difficult time understanding how someone who has known and interacted with God as a Person could later deny His existence, and I can comprehend even less how anyone could go from loving to hating Him. But that aside, exbeliever has insightfully pinpointed something very important—at the core, the difference between us is a matter of the way God tastes to us, not the intellectual question of His existence. I've found this to be the case over and over as I've read and listened to the outspoken atheists of our time (Hitchens, Harris, etc.). The conversation turns inevitably and repeatedly to the horrific nature of the Christian God. In debates, intellectual questions about existence consistently take a backseat to this objection, and every aspect of the debate absorbs its flavor.
What does this mean for us as we speak to these atheists? In the end, no person's taste for God or the gospel will change unless the Holy Spirit changes his ability to taste. But the Holy Spirit moves people when we explain and glorify the beauty of God and the gospel, so we need to make a more concerted effort to, first, in the midst of every topic of our apologetics, keep the arguments close to the idea that we're ultimately conversing about a Person—a real Person whom we love, Who is distinct from us, and Who has a will and purposes; and second, we need to focus on understanding, explaining, and honoring His character and actions. I've come to believe that this is where we need to begin, even before arguments for His existence. This is where we need to concentrate our speaking and writing.
Further, within this core issue of God's character, I believe there is a truth even more deeply central to the divide between Christians and atheists—God's surpassing holiness. I'm convinced that the atheists' inability to comprehend God's holiness is the particular turning point from which they have gone completely wrong. If the Holy Spirit were to reveal a glimpse of the majestic righteousness and holiness of God (and, by comparison, our sinfulness) to these atheists, the answers to 90% of their questions would fall swiftly into place. Since the Holy Spirit often uses our words as the means by which He reveals such things, we need to be prepared to speak on this subject.
To that end, if you haven't read The Holiness of God by R.C. Sproul, I recommend you begin there. Next, you must read the Bible all the way through. Over and over. And over. You must know God from every angle that He has revealed to us, and you need to wrestle with what you find there until the perfect pieces fit together clearly enough for you to help others put their own pieces together. If you don't feel the goodness and beauty of God in your very bones, now is the time to seek it out.