It is in my opinion that the moral argument for God’s existence is perhaps the simplest to understand, although it has shared a complicated history among philosophers . Of course, the depth and detail of the argument may require some understanding in certain respective moral theories (deontology, utilitarianism, virtue ethics, etc.), but the scheme is nonetheless an overall system of deductive simplicity:
- (1) If God does not exist, objective moral values and duties do not exist.
- (2) Objective moral values exist and duties do exist.
- (3) Therefore, God exists. 
Mortimer Adler in his book, Ten Philosophical Mistakes  outlines our terms needed:
[L]et me make sure that all of us understand as clearly as possible the meaning of such terms as subjective and relative, on the one hand, and such terms as objective and absolute, on the other hand.
The subjective is that which differs for you, for me, and for everyone else. In contrast, the objective is that which is the same for you, for me, and for everyone else. The relative is that which varies from time to time and alters with alteration in the circumstances. In contrast, the absolute is that which does not vary from time to time and does not alter with alterations in the circumstances .
Thus, in respect to the first premise of our argument and the writings of French philosopher Jean-Paul Sartre, “If, however, God does not exist, we will encounter no values or orders that can legitimize our conduct” .
It is then the case of some (if not most) theistic beliefs that moral values, knowledge and foundations are reliant upon the existence of God. The argument as seen above can be found in C.S. Lewis’ famous work, Mere Christianity . The thrust of Lewis’ argument can be found on the first page:
“How’d you like it if anyone did the same to you?” – “That’s my seat, I was there first” – “Leave him alone, he isn’t doing you any harm” – “Why should you shove in first?” – “Give me a bit of your orange, I gave you a bit of mine” – “Come on, you promised.” [ … ]
Now what interests me about all these remarks is that the man who makes them is not merely saying that the other man’s behavior does not happen to please him. He is appealing to some kind of standard of behavior which he expects the other man to know about. And the other man very seldom replies: “To hell with your standard.” Nearly always he tries to make out that what he has been doing does not really go against the standard, or that if it does there is some special excuse. [ … ] It looks, in fact, very much as if both parties had in mind some kind of Law or Rule of fair play or decent behavior or morality or whatever you like to call it, about which they really agreed. 
Lewis, thence, in structuring his argument outlines a couple particular notes of the human disposition:
- (1) Man as haunted by the idea of a sort of behavior that they ought to practice; what might be called fair play, or decency, or morality, or the Law of Nature.
- (2) That they do not act in accordance with that Law or Rule. 
In respect to (2) Lewis gives a brief explanation. Unlike the law of gravitation for instance, where we see that it describes how a given stone falls when dropped, this “Law of Nature” says what men ought to do and do not. Morality cannot be used to describe the behavior of men since they do not act in accordance with this Law, but must rather be applicable to prescription instead.
Thus, the existence of the given Law seems to be a strange notion. He later goes on to inquire “whether the universe simply happens to be what it is for no reason or whether there is a power behind it that makes it what it is” . Before answering this question, Lewis has a question regarding observed facts and the universe:
There is one thing, and only one, in the whole universe which we know more about than we could learn from external observation. That one thing is Man. We do not merely observe men, we are men. In this case we have, so to speak, inside information; we are in the know. And because of that, we know that men find themselves under a moral law, which they did not make, and cannot quite forget even when they try, and which they know they ought to obey. 
Lewis then continues by saying that if this power behind the universe were to exist, that it itself would not be one of the observed facts “but a reality which makes them, no mere observation of the facts can find it.” However, this outside reality itself could show itself to us as one of the observable facts of the universe – in the same way that an architect of a house could be a wall or a staircase.
The only way in which we could expect it to show itself would be inside ourselves as an influence or a command trying to get us to believe in a certain way. 
Thus, Lewis goes on from here to stipulate that a Power behind the facts does exist; a sort of Director or Guide .
Lewis’ argument is easy and helpful to use in terms of personal evangelism and having a good grasp of the argument overall. I do think that arguments for more complicated theories of ethics (I tend to lean more towards Virtue Ethics (VE) myself) are more fruitful for discussions on natural theology than the mere evaluation of Lewis’ argument.
J. Budziszewski, Mark Linville, Stephen Pope, Jean Porter and many others have done great work in the area of Natural Law, Virtue Ethics and moral arguments. To gain interest in this argument I would really start with C.S. Lewis and work your way up with others.
-  Mark D. Linville (2012) has exhausted this matter in his essay on the Moral Argument in The Blackwell Companion to Natural Theology (Wiley-Blackwell: 2012) see p. 391
-  Cited from William Lane Craig in his essay, Richard Dawkins on Arguments for God in God is Great God is Good, ed. by W. L. Craig and Chad Meister (IVP Academic: 2009) p. 18
-  Mortimer J. Adler, Ten Philosophical Mistakes (Simon and Schuster: 1985)
-  Ibid., p. 110-111
-  Jean-Paul Sartre, Existentialism is a Humanism (Yale University Press: 2007) p. 29
-  Quotations will be drawn from C.S. Lewis, The Complete C.S. Lewis Signature Classics (HarperOne: 2002)
-  Ibid., p. 15
-  Ibid., see p. 24
-  Ibid., p. 30
-  Ibid., pp. 29-30
-  Ibid., p. 30
-  However, it should be noted that by “Power” Lewis does not mean the God of Christianity. He clarifies this point on p. 31, where he writes that “I am not yet within a hundred miles of the God of Christian theology. All I have got to is a Something which is directing the universe…”