One of the most common objections---perhaps the most common objection---that religious people have towards Secularism is that, without God, there can be be no basis for morality. Essentially, this argument means that there can be no moral system that humans can create and live by that is derived from a rational set of principles, and, thus, a moral system can only be imposed from outside of the human experience by a god. Which, by the way, proves that there is a god that exists. The follow-on corollary is usually that, if there wasn't a god, we'd all become cold-blooded murder machines. It's odd that this argument comes up so often, especially since it's pretty easy to refute. So let's take a little trip down the path towards constructing a working theory of secular morality.
The first step we need to take along that path is to define what, exactly, morality is. Wikipedia defines it as
...the differentiation of intentions, decisions and actions between those that are distinguished as proper and those that are improper. Morality can be a body of standards or principles derived from a code of conduct from a particular philosophy, religion or culture, or it can derive from a standard that a person believes should be universal. Morality may also be specifically synonymous with "goodness" or "rightness".
Religion posits a set of externally imposed set of proper actions. This imposition may or may not be congruent with human nature. For instance, "Masturbation is a sin". For all of human history, even in Christian societies where this statement has been generally accepted as correct, I think it's safe to assert that this decree has been almost universally disobeyed. I mean, let's just say that I spent a large portion of puberty praying for forgiveness for "sinning".
So, what benefit derives from obeying this ban on masturbation? What unwanted consequences can be derived from breaking this moral command? Well, with an externally imposed moral system, who cares? We don't even have to ask questions like that. Masturbation is banned by God, so we no longer even need to think about it (though we will, constantly), nor are we allowed to question whether our god was correct or right for imposing that ban upon us. We've been given a command, and we no longer have to give any thought to that issue. "God says so", stops all thought.
A larger question also arises from an externally imposed moral system, which is, who is the system designed to benefit? Is it designed to benefit us, or is it designed to benefit the god who imposes it? In the case of Christianity, these moral commands are imposed by God, who desires us to freely worship him, both in this life, and the next. The design of Christian morality is to set the proper bounds for action to both claim and maintain salvation, and ultimately, to provide God with the kind of worshipers he desires. One may argue that a variety of benefits are derived, secondarily, by Christians who live within the bounds of proper action imposed by God, but they are not the primary beneficiaries. The benefits they derive are rewards for their part in providing the primary benefit to God, for whose benefit the system was imposed in the first place.
We can show this, by the way, by looking at a simple example of how we do not benefit, at least in this life, by obeying the commands of our god. For instance, what if God says---as some of his followers assure us He has said---that we cannot eat pork or shellfish, because it's unclean. If I'm starving to death by a plate of bacon-wrapped lobster, therefore, I cannot morally eat it. My choice is to die, and enter the afterlife to bask in God's glory, or to offend God, and risk eternal damnation and suffering. If I starve and die, that works to God's benefit.
Finally, we cannot easily alter an externally imposed system of morality. If God has decreed it, how can we possibly change it, even if it no longer works? We either need a new revelation from Vishnu, telling us that he's changed his mind, or we can pretend that Yahweh didn't really mean the bit where He said "Ixnay on the Obsterlay". Indeed, the only reason that Christians can eat pork today, is because Peter supposedly had a vision where God showed him a herd of unclean animals and said "Rise, Peter, kill and eat." Peter didn't want to do it, but God kept nagging at him until he agreed. If that little story had been lost from the book of Acts sometime in antiquity, pig farming would be a remarkably unprofitable occupation in the Western world. Luckily, God changed his mind. (Or Peter secretly loved lobster. We'll never really know.) Only an updated revelation put bacon on the plates of Christendom.
Secular morality, on the other hand, would have precisely the opposite characteristics, to wit:
We can derive such a moral system rationally, simply from the evidence of human nature as we generally observe it. Now, I don't wish to imply that these observations of human nature are universal. In any human population, there are always outliers, such as psychopaths or the insane most obviously, and, often less obviously, people who, for one reason or another, place their own desires above those of all others, no matter what the consequences: Criminals, sadists, and the like. Of course, it is precisely those people who make a system of morality, and its extension, a system of justice, necessary.
Normally, though, all human beings share the same experiences. We all experience happiness and joy when reuniting with long-lost friends. We all grieve at the death of a loved one. We all experience anger when someone eats our lunch out of the office fridge, which we had waited to eat all morning! Beyond that, we instinctively know, even as very small children, that we dislike painful, and unpleasant things, and we enjoy pleasurable and fun things. Moreover, we value ourselves, and thus we all know how we'd like other people to treat us, and we dislike it if we percieve that others treat us unfairly.
Indeed, this sensitivity to fairness seems fairly innate, and becomes apparent at a very early age. For instance, take a couple of six year-olds fighting over how to share a candy bar. Tell them that one of them must cut the bar in two, and the other one will get to choose whichever of the two pieces he wants. You will never see a candy bar apportioned with such micrometric precision as you will when the first kid cuts that candy bar. Since someone else gets to choose the most desirable portion of candy, the child who's cutting the portions responds to the incentive to maximize the fairness of the apportionment.
Look, let's be honest, the sense of "fairness" could also be characterized as a sense of selfishness, or, to put it more politely, self-interest. In other words, I don't want anybody else to have something more than me, unless I have some sense that they really, really, deserve it. And maybe not even then. So I will cut the candy bar in a way that others will percieve as equal. The best I can get is exactly half of the candy, so I cut it in such a way as to maximize the amount of candy I get.
Because we value ourselves and have a a sense of fairness, or, at least a sense of self-interest, we all assign, in our minds, the term "bad" to situations where were are harmed, suffer loss, or caused to suffer by the actions of another. Similarly, we assign the term "good" to actions that help us, or provide us with other benefits. We already have the first individual assignment of moral goods and evils based on whether we are personally harmed or benefited. This arises naturally from being self-aware, and having an interest in making life as good as we can for ourselves.
We know, of course, that this self-awareness, and the assignment of things as good and bad in our lives is not unique to us personally. Everyone else is also self-aware and has the same personal power of value assignment. It follows then that these characteristics are rooted in human nature, and thus are universal to the human race. We can recognize that everyone wishes not to be harmed and wishes to be benefited, which allows us to move the concept of a personal good or bad, to a human-wide good or bad. After all, if I don't wish to be bludgeoned to death by other people, then other people must not want me to bludgeon them to death, even if I really want to. It is in my interest, therefore, to enter into a general agreement with other people not to bludgeon each other to death. Thus, we each increase our own sense of safety and well-being if we all agree that bludgeoning each other to death is bad.
Let us imagine then, as Sam Harris has suggested, a world in which every human being suffers the greatest amount of suffering and pain that they can possibly bear, for as long as they possibly can, before dying. The entire experience of life is the worst suffering you can possibly bear, from birth to death. Obviously, this would be the worst of all possible worlds. Imagine being on the 110, trying to get to LAX at rush hour, every single day. It would be horrific. Reducing that suffering, even to the most minute degree, for even one person, would be a positive moral good.
Since no one wants to suffer, increasing someone's suffering, even in the smallest degree, would be a moral evil. We have, then come upon a secular moral precept---a very simple one, and one from which all others derive---that it is immoral to harm someone else, as all harm causes suffering to a greater or lesser degree. This principle, in addition, provides us with a scale on which to judge the relative evil of an act. The more suffering that an act causes---the closer it draws us towards the worst of all possible worlds---the more morally evil the act is. Having defined a rational principle of evil, the principle of good is logically derived as its opposite action. An act that reduces another's suffering or that helps another is defined as morally good.
We now have set of basic moral principles that give us general guidance on what good or evil is, and that meet two of the three characteristics I mentioned at the start.
Because this system derives from observable human nature, i.e., our self-awareness and the natural sense of fairness---or, if you prefer, self-interest---that partly comprises it, and which we all share, it is an internally imposed moral system. We can accept it because we can, based on whether another person help or harms us, intuitively determine whether what they have done is good or evil, and we can know whether we have done good or evil to another person, without reference to some third party's codified instruction. Because this system judges good or evil based on whether people are helped or harmed, it benefits us directly, and not some third party. It judges the rightness of an action based on the effect the action has on us, or on mankind as a whole, of which we are a part.
That leaves us with the third characteristic, which is our ability to change our views on what is moral or not. Because we're human, we are deeply flawed. As a result, at different times, or in different ages, we might see the same act differently. We may have done harmful things in the past because, being flawed and fallible, we simply didn't recognize them as harmful. Similarly, we may have seen things as harmful that we now know are not. Or we may merely observe that some practices simply don't work well. But, whatever the reason, because this secular system of morality is self-imposed, then as our knowledge changes, we can naturally change our moral views to accept this new knowledge, without having to reference the wishes of a distant or hidden third party. Indeed, not only do we not need a moral system externally imposed on us by Zeus, or Odin, or L. Ron Hubbard, I'd argue, as Matt Dillahunty does, that a secular system of morality is both rationally and morally superior to an externally imposed one.
Of course, what I've presented here is only the broadest outline of a rational moral system. The devil is, as always, in the details. Is it moral to harm another person when defending myself from them? How do we treat animals? Do we firebomb Dresden to defeat the Nazis? Should we have public beatings for people who drive at 50 MPH in the left lane of the freeway? There's an entire universe of moral questions that have to be examined under a secular moral system. That's no different than the ethical quandaries that have plagued religious societies from earliest antiquity. But, at least, under a secular system of morality, we can answer those questions ourselves, without having to wait around to see what a monumentally uncommunicative Mithra or Ahura Mazda thinks about it.
And that's a pretty good start.