I think we've mixed two issues here: how we can be good w/o God, and why we should be good without God.
I think the first question makes the most sense if we ask how we are good with God. If we're being good because we know we'll get a reward in the afterlife (typical reason for believing in God), that seems to be the same amount of goodness as being good because we know it'll be beneficial to us. And if God is the source of ethics (or, more radically, if God is the ethics), all we've really done is assume that our methods of getting at these codes (stereotypically, the Bible) are reliable. So really I don't think bringing God into the equation is making the issue any easier. Godless ethics would come from a desire to be good or from a desire to be of service to others, and ultimately one could trace that idea of where the ethics is coming from back to their (psuedo) metaphysics and epistemology.
Since I'm probably getting a little cryptic and abstract here, I'll try giving an example from my own life. I think that the way to be moral is to adhere to standards that bring the greatest benefit to others. What is the greatest benefit to others? I would argue that it is the nurturing of their own self-actualization and expression, because ultimately that will bring the greatest fulfillment to the individual. Now then, how did I come up with this answer? Simple, I used my reasoning capabilities and have looked at the issue in all the angles I can think of, and this is the code I came up with. How do I know that this is actually true? That's where we get into epistemology: in this case, I'd say "reason as supreme" in regards to knowing anything.
Now, let's get to the second part. Why should I seek to benefit others? Why should I be good? This part sometimes is necessary to avoid if we want to actually be doing good (like if you adopt Kant's perspective in which all good comes purely out of duty). But let's ignore that issue, because I don't like it (I don't think that self-interest must be absent to do good; in fact, I lean in the opposite direction). The first answer is, well, because I actually will benefit from it purely out of enjoying the act. Let's consider altruism: is altruism a state in which we help others for the sake of helping others (i.e. we get our reward directly from it, presumably through feeling joy)? Or is it a state in which we help others and we get absolutely no benefit/pleasure from it (i.e. duty)? A case could be made for either, but I would actually say that the latter is a vice on grounds that it is degrading to the person who does it! Why is self-degradation evil? Because to measure the good of any action, I look at what happens if we universalize it. If everyone is using themselves for the good of society, we all are suffering needlessly. Rather, the only way we can create a net good is through the first version of altruism.
I suppose to wrap up I'll have to add that actions that are immoral are acts that do not simultaneously respect the Self and others, in case my argument left you wondering what would or could possibly be immoral in that situation. Immorality stems from ignorance, shortsightedness, inability to overcome inertia (laziness), and failure to override basic inclinations (fear, rage, etc.). I should add that somewhere in the middle here I shifted from talking about ethical theory in general to my own ethical theory, which is why I'm saying what is and is not immoral. In short, I would say that it is logical to be moral, and that 'morality' coming from any other thing should be regarded with skepticism. And to finish up with what I said on altruism, I'd like to point out that people who are not naturally inclined to be altruistic must find their own ways to mediate between their own needs and the needs of others to be good, perhaps finding a unique way to contribute to the community at large. There should be a way for everyone, because we are all social animals and can derive joy from some type of helping people.
Phew, okay. As you can see, I love thinking about ethical theory. What I wrote is probably still a mess, but do ask me to clarify anything that makes little to no sense.