For me, the first logical argument of morality seems to extend from the golden rule. We act morally towards others because we would prefer to receive those same actions. Quick examples would be stealing, lying, or physical abuse. We can recognize that it is better to live in a society where those actions are discouraged, so that those actions aren't perpetrated against us. I believe it was C. S. Lewis that made the claim that the first form of morality that kids understand is fairness. I see the concept of fairness as a logical argument not a transcendent standard, although I'm sure that Mr. Lewis would see it otherwise. I think the answer is somewhat obvious, ask yourself how you would like to be treated. If you were black, would you think slavery is a good thing? If you were a woman, would you think it's perfectly fine to be treated as a second class citizen? If you held different beliefs than those in power, would you think it's fine to have other's beliefs forced upon you? The best way to design a moral system is to not know where you might be in that society. If you could imagine yourself in any position in that society and still think you are being treated fairly, than your system is off to a good start.
Generally, when the moral argument comes up in conversation with my Christian friends, the argument that they pose is that Christianity has a transcendental standard, the Bible, which of course comes from God. They claim that their standard is the true moral standard and all others fall short. Any disagreements or contradictions I have pointed out between what they claim to be the standard and God's own actions in the Bible have resulted in various apologetic rabbit trails. God, they claim, is not subject to this standard. At that, I'm left scratching my head. The argument is no one is equal with God, so God's actions are unquestionable.
This thinking pulls us right into the Euthyphro dilemma. Is God's standard based on something apart from God? If so, then God is unnecessary to create that standard and we can develop the standard apart from God. Or, is the standard based on arbitrary decisions that God has made? Is killing only wrong because it's commanded to be wrong? So, if it wasn't commanded to be wrong, it wouldn't be? We've never come to a successful conclusion to the Euthyphro dilemma debate and so it wouldn't be worth restating the circular arguments we've had.
If the Christians are going to claim that there is this "transcendent standard" I would like to know what it is. Every Christian I've spoken with has a different idea about what rules in the Bible are important and which ones aren't. I suspect Christians get their set of morals in the same way non-Christians do. We have parents or guardians that raise us to obey the rules. We grow up and reason out how to live in a society. When we disobey the laws of the land our actions are met with consequences, just as when we break social norms. And, from all the input we get growing up we begin to develop our own sense of morality and attempt to pass that on to our kids allowing them to start the same cycle we've gone through. The Christians claim they've received their morals from the Bible, but instead I see them picking the parts of the Bible that fall in line with their own morality and discarding the rest. I would even admit I did the same thing as a Christian, but would never admit to it while I was a Christian.
It's a good thing that we developed our morals in this manor, because if we lose our faith in God, as I did, we don't have to lose our morals. They were never based on the Bible in the first place. We had reasons outside the Bible for why we should act in society the way we do. There were a few things within my moral system that did change when I lost my faith, but of those things that changed, I never had a reason apart from the Bible to accept them in the first place, and so they were easily discarded without any damage to my central moral system.