For if the person does not believe in God, God's commandments mean nothing to him. However, my efforts are not doomed to failure. I still have two things working in my favor. It may be that I believe in the God of the Bible, and he does not. But if we both accept the validity of reason, then we have a common ground for discussion.
Reason acts like a universal language.
In other words, every moral norm does have a rational explanation. It has reasons behind it. So, if I want to convince this person that adultery is immoral, all I have to do is give him the good reasons which support my claim. If the person speaks the language of reason, and is open-minded, he will accept the reasons and agree with the conclusion. Now, as I have done with the man in the example above, so has the Church, in the Second Vatican Council, done with the modern world.