This is going to be an unpopular statement, but: they don't. Not because humans are incapable of forming moral frameworks based on their own reasoning, but because among them, atheists don't actually exist; we're simply not wired for it.
Broadly speaking, we can divide the gods into three categories: the supernatural, the natural, and the artificial. The supernatural are what most people think of when they hear the word "god": Yahweh, Mazda, Zeus, guys like that. Their existence is a matter of faith. The natural gods DO exist; they're Power, Pleasure, Fear, and so on. The artificial are mostly refinements (often presented as aspects or avatars) of the other two categories. They, similarly, do exist, but rely on humanity for their creation, and usually their sustenance: Status, Approval, and of course, the Almighty Dollar.
You are, likely, dubious, claiming those aren't worshiped in the same way that the supernatural gods are. Experiment, then: take a thick wad of single dollar bills, walk on to a busy road's overpass, and toss them down, one by one- you'll people run into traffic to grab them, risking their health and their lives for what they could get with just a few minutes' work (as per local minimum wage laws). If it walks like a god and quacks like a god...
All that said, if you only practice moral behavior for fear of retribution (be it from god or government or any other external entity), then are you really being moral, or just cowardly?