Rocky, I'll bite. Mostly because I recently came to a new job with a credulous Christian who looked at an athiest as some sort of alien, and had much the same question. Pointing out that 80-90% of the planet gets along just fine (or at least as fine in many ways) as the Christian bunch (many of whom believe wildly divergent, and mutually exclusive things, (a Christian Scientist, a Unitarian, a Catholic and a Mormon walk into a bar...), had little effect.
So, here goes. I won't pretend that there is some universal athiest handbook of morals or ethics (different things, BTW). One of my favorite qotes about religion (paraphrasing here) is that of all of the tens of thousands of religions that have ever existed, I'm only an athiest about exactly one more than you are. Most likely you don't believe in Thor, Zeus, Krishna, or Ceasar, for that matter. We have a lot in common :-)
Much of the "morality" that I teach to my kids is basically Kant's categorical imperative, which is just a fancy version of the golden rule: "Act as if your actions were the law for everyone" This isn't just "hey everybody else is doing it, so why shouldn't I?" What if everyone cheated on their taxes? What if everyone spouted off statements that were just a little bit racist? What if everyone refused to help a person in need?
When I think this way, and not simply "How would I be affected?" on the whole, I tend to try to treat everyone, whether they are like me or not, at least as well as someone who is a friend of mine. Not perfect trust, but more than seems to be the average.
So what would athiests do about laws? Exactly what we are doing now. Find the things that are intolerable, and punish those, and leave everything else alone. Most of the injunctions in the bible are not enforced by law, or even community standards. For more on this see: www.godhatesshrimp.com Prepare to be insulted if you take every word in the bible literally (hint: you don't).
I understand explicitly that society cannot exist without rules, and at least some agreement on what is the "common good". I do find many religious people do a great deal of good work, for which I am greatful, and thankful, and I tell them so, when I get a chance. But use the power of government to enforce rules set down thousands of years ago, by a pre-scientific, mostly pre-literate, supersticious bunch, makes no sense to me.
I'm down with "Thou shalt not kill", but coveting your neighbor's ass (more likely his Jag or Corvette if you prefer, in a modern context). is practically the national sport. I don't believe I have any ethereal soul to lose, but I do have children and hopefully some day grand children, etc. They are reason enough to want to leave the world a better place, and show them (and anyone else paying attention) by way of example, that being nice to each other just isn't that painful.
Hitch can be a boor, and Dawkins, who is a personal hero of mine, gets unjustly maligned, but even though I have many dear friends and family members who are true beleivers, I agree with them that, knowing what we know now, we should move beyond religion. It is just one more way to create conflict where none really exists. And, the way it is going in this country, at least in the last decade, there is a definite danger to the overall scientific literacy of our society, by (among other things), trying to hold up "intelligent design" as a co-equal "theory" to evolution.
As Dawkins points out, this is a semantic trick by the pushers of ID conflating the common use of the term "theory" which can be used to describe any old crackpot idea (See: my theory about all of the missing socks forming an island in the Pacific) and a true "scientific theory" which is continually tested and refined. Belief by nearly all serious scientists in evolution reflects not some orthodoxy, but rather consensus that the methodology and findings of thousands upon thousands of studies, research, and debate are sound. The same cannot be said for ID.
A little off point from your question, but this type of disengenuity is part of the reason that athiests get a little prickly. I don't get offended until someone tries to take over a school board :-)
Cheers,