Entirely depends on the situation. If a random person out of the blue says this, more often than not they are desiring to engage in some type of dialouge about it. I would take that as an opportunity to witness to that person. I often pray that somehow, someway, I can be a blessing to someone that day. Given my situation, I don't get many opportunities after losing my license. I go to work, church, and home. Any opportunities I get I will usually try to take advantage of. The few times I have tried I feel like I have failed; I can always think of 1,000 different ways I could have handled it better, or said something different.
If it is someone you know, I would feel even more compelled to witness. If that person knows you and has been around you, it can be a challenging and even embarrassing situation (if) you haven't been living and acting like you should (the "you" here is ANY Christian, of course).
After accepting Christ, I told my cellmate my testimony before being released. I told others as well, but I'll never forget his response. He certainly didn't attribute it to God, told me I finally 'made peace' with my situation there and basically "worked it out in my mind", or things to that effect. I didn't press the issue. I would certainly love a do-over.
Since "I don't believe in God" is a statement and not really a question, the response could be an "ok" or a polite 'head nod'. But I can't imagine any Christian not following up in some way. Again, depends on the situation, but I would hate to regret it later if I did nothing.
Asking them "why not" would be the most logical to start and see what deveops. You could also start with, "Well, this is what God for me" and see what unfolds. The key is to BE READY. 2 Timothy 2:15 "Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth".
Another option is to remind them of beautiful paintings, buildings, all the wonderful technology that man has invented. Remind them what they all have in common, a CREATOR. The creation argument is a divisive one, but you never know if a seed will be planted.
Being hit out of the blue like that is challenging; that's why knowing God's Word is your best resource. Some would bombard the person with scripture, which I'm not sure is the best way to go. Knowing key verses can be invaluable though, again, possibly planting a seed.
As far as your question goes, I'm assuming you are referring to getting into some type of debate with a fervent atheist. And yes, most likely there is little we can do or say to change their mind. I took the question at face value and answered that way. Either way, I would feel compelled to give some type of response. You have to remember that they arent rejecting you, they are rejecting Him. Mark 6:
4 But Jesus, said unto them, A prophet is not without honour, but in his own country, and among his own kin, and in his own house.
5 And he could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them.
6 And he marvelled because of their unbelief. And he went round about the villages, teaching.
