18th century philosopher Immanuel Kant championed moral arguments for the existence of God, as part of his larger deontological ethical framework. In his "Critique of Practical Reason" he argued that if achieving perfect happiness was the ultimate moral goal, then it could only be so because a God would have the power to provide for such a state of affairs.
The moral argument implicitly rests upon accepting moral realism and, in particular, Divine Command Deontology as the only possible source for moral realism. It takes a very simple form but is nonetheless emotionally appealing to many. Moral realism refers to the idea that there are objective ethical statements that ought to be pursued. Deontology is a subset of theories in normative ethics which postulate that to be good is to fulfill some pre-established duties, regardless of what consequences might be triggered from those actions. So for example if lying is trulybad, Kant argued, one must refrain from lying even if it seems to us that we could achieve a greater good (say saving someone's life) by doing it. Divine command theory is a form of deontology whereby the aforementioned duties are equated with what a hypothetical God wants from us. An argument from morality begins from the conclusion that moral realism is true, and moreover that this could only be so if there's a divine being to ascertain and distinguish good from evil.
Euthyphro dilemma Plato rejected moral arguments on the basis that divine opinion is no better a source of absolute values than human subjectivity, God being a subjective being by definition. That is, simply saying that a deity prefers certain actions falls short of proving the deity's preferred value ought to be intrinsically good. On the other hand, if certain values were intrinsically good that would have to be the case regardless of whether a God recognizes them or not.
If absolute moral values exist they come from God's authority. Absolute moral values do exist. Therefore God exists.
Rejecting the premises
Premise 1 postulates that divine command deontology is the correct ethical theory, yet provides no proof that all of the alternative theories are false (contractualist deontology, any form of consequentialism, etc.) Premise 2 is false if morality is subjective (relative to the observer) or if moral nihilism is true (no values exist whatsoever).