I am writing this based on the fact that I have had similar questions asked recently by multiple people. I've even spent a couple hours watching a group of "believers" argue with another person over the topic.
The issue at hand, is how to do you talk to an Athiest about God. Many (not all) are well educated and have done a lot of research to back up why they believe God cannot exist. One approach I havn't seen many take, is the one that I am proposing.
First and foremost, you can never win a "logical" or "intellectual" debate with someone who says God doesn't exist. I would recon it to Jesus talking about how the sick go to the doctor. If the person doesn't believe they are "sick" and need a "doctor" your points will be mute. Many of their "logical" explanations can't be argued without having an in depth understanding of each of the topics they want to discuss.
Your only real answer to someone who wants to debate is your own story. Even then it's not really a debate, but rather a journey. The Bible is full of stories and for good reason. They teach us about other people and their struggles and successes. They also teach us about the power of one's story. If you know your story and can share you story and what God has done, it doesn't really matter what point they are trying to make. They can't take your story from you and you can share what God has done in your life.
There is so much more than just believing that there is a God. Rather it is believing God...believing Jesus. Even the demons believe IN Jesus. Our story takes our believing Jesus and makes it real...makes it personal. It is our proof that there is a God and that He is a personal God.
Share your story, be a good friend, and love the person. Often times it is through that love that the friendship grows stronger. The friendship will lead to a strong relationship that will allow you to share your story. The story is your proof that God exists. Your story is the what will help them believe that they need the true "doctor."