There are people in the world who still believe that atheists can't be moral. There are more still who acknowledge that we can be moral but don't understand how we can be so without the "Judeo-Christian" moral framework in which we Americans are so often raised.
This post will show you how I, as an atheist, make moral decisions. Other atheists may do things differently.
Today Nathan and I went grocery shopping. We turned an aisle and spotted a wallet on the floor. He handed it to me and I could see that it belonged to a white woman with dark hair. It felt very compact as if it had money in it or, at least, maybe some credit cards.
First I asked myself, "How would I feel if I lost my wallet?" The answer is afraid. Why? Because someone would have access to my identity, my money, and my private information (address, spare key, etc.).
Second, I asked myself, "What would I want the finder to do if I lost my wallet?" The answer is: turn it in. Don't take the money and credit cards. Don't write down or memorize my private information. Don't take my spare key. Don't rifle through my wallet and look at my kids' pictures (if I had kids). In other words, don't violate my privacy. Just take it to Customer Service and let me claim it intact.
Based on these thoughts (which took only a couple seconds to form), we did just that. We turned the wallet in without pilfering or stealing. The only thing we knew about the lady was her general appearance because that portion of her driver's license was visible on the outside.
After we turned the wallet in, I continued to look around for the lady. We ended up seeing her in the checkout line frantically searching her bag. Nathan asked her if she had lost it (just to be sure it was her) and she said yes. We told her it was at the front desk and she thanked us. The matter was settled.
At no time did we think about Moses writing his Ten Commandments. Neither did we think about how Yahweh might punish us if we stole. It didn't even really occur to us to steal because we are heavily grounded in a secular morality based on doing what is good and not doing what is harmful. Why do we not steal? We don't want people to steal from us. Why do we return lost property? We would want someone else to return our lost property to us.
It's just that simple. No gods, no divine wrath, no eternal punishment needed.