Debating atheist philosopher A. J. Ayer, an Anglican Bishop exclaimed that if Ayer didn't believe in God, "then I cannot see why you do not live a life of unbridled immorality."
Well, I'm an atheist, and I do live a life of unbridled immorality. I eat pork and shellfish, ham and cheese. I wear cloth of mixed fibers. I work on the Sabbath, all of them. I've had premarital sex, and I liked it. I divorced my first wife, to our mutual benefit. I'm not gay, so I don't have sex with men, but if I were I would and feel no qualms whatsoever (and if you're gay, it's none of my business). I drink beer and coffee. Back in the day I used to smoke a ton of marijuana; I quit only because (dammit!) it now makes me sick. When and if I'm terminally ill, in great pain without hope of recovery, I'll have no problem at all committing suicide, and I expect—no, I demand—that my physician assist me.
In general, I live my life to please myself, not God. The theists are right: Without a God, the sort of arbitrary, purposeless strictures that constitute most of their "morality" make no sense. Since I'm an atheist, I reject those purposeless strictures.
So why do I follow those strictures that do make sense, that are purposeful? Well, stated that way, the question is self-answering: I follow them—and I expect others to follow them—because they actually do make sense. Rocket science, eh?
I don't kill people because I don't want to kill people—I'm sentimental and squeamish. I don't steal things because I don't want to, I don't rape, drive drunk, commit mopery on the high seas, etc. because I don't want to. It doesn't matter how it came to pass that I don't want these things—evolution, socialization, rational deliberation or the accidental wiring of my brain—it is an actual fact that I don't want to do most things that normal people disapprove of, because I'm a normal person. Furthermore, I don't want anyone to kill me, I don't want anyone to steal my stuff, it makes sense for me to pay for police and prisons, and it makes sense for me to submit to strictures that are in line with what I already want. I gain much and sacrifice nothing (or nothing much) by preventing myself from killing people.
My neighbors approve of most of my behavior: I have the same sort of brain with the same evolutionary history, the same sort of schooling, the same sort of upbringing and social conditioning, have read the same sort of history, literature, movies and television as 95% of my neighbors, and surprise, surprise, surprise, I have the same sort of preferences about my own and others' behavior. How could science explain that!?
There are a few other activities about which the U.S. government and the state of California and I do not see eye to eye, 'nuff said, but I'm mostly law-abiding. I'm a statistically normal person in a democracy. By definition, democratic laws tend to reflect the attitudes of normal people. My attitudes establish the law; the law doesn't establish my attitudes.
[Update: I accidentally cut the following paragraph; it helps make sense of the subsequent paragraph]
When I was on my way to Pakistan for the first time, I made the mistake of mentioning to my seat-mate that I was not religious. I was treated to a forty-five minute diatribe which can be condensed down to the argument: You have to believe in God so that—and I shit you not, he used this exact example—you'll know it's wrong to have sex with your sister.
This theistic argument is—like all the other theistic arguments—mind-numbingly stupid (the only sophistication you'll see in theistic arguments is in hiding the stupid parts). If the only reason I don't have sex with my sister is just because is says so in the Koran, then why don't I not want to drink alcohol just because it says so in the Koran? On what basis am I choosing? Contrawise, if there's an alternative cause for my not wanting to have sex with my sister, I don't need to read it in the Koran.
I know, Quantum Mechanics seems simple in comparison.