I. If God Does Not Exist, then Objective Moral Values Do Not Exist
"Objective" means something is true (or false) regardless of what anyone thinks about it.
If the universe consists of matter and energy bopping aimlessly about, which occasionally clumps together into planets, stars, life, etc, then there are no objective oughts. That is to say, moral values would be merely personal or social opinions and preferences, but would not exist in any factual form since a purely naturalistic universe would not have any direction, plan, or anything one ought to do, objectively speaking. We would create our own moral values, and they would be just that: our own creations.
II. Objective Moral Values Exist
But objective moral values do exist. The rape of a child is not socially unacceptable behavior; most humans would agree that it is morally reprehensible. Most people agree that even if everyone were brainwashed by the Nazis to believe that the Holocaust were right, the Holocaust would still have been wrong.
Also, we perceive a gradual improvement in morals through history, from barbarians who practiced human sacrifice, and slavery, up to today where we see that we are much improved in the way we behave. So we are slowly discovering what is right and what is wrong. If moral values were mere social conventions, then it would be more like fashion. We would perceive change (and the perennial coming back into style of older fashions), but not the improvement that we do actually witness.
III. Therefore, God Exists
And the conclusion follows logically from the two premises: God exists.
This is a very brief intro. For a more in depth look, see the full article.