Non-theists will do what is right for the same reason non-theists can have moral values. Theists often ask the rather odd question; "How can you have morals without God?", as if doing or not doing certain things simply because God says so would be morally right.
- If the only reason one is moral is because "it says to do so in the scripture", can it really then be said that that person is a moral person?
A non-theist does not live in a vacuum either; his/her actions will cause reactions from the surroundings, some negative, some positive, Non-theists have parents too! We all know what is wrong basically because doing wrong things (on this basic level we're talking about here) is destructive and harmful to others. This can then - by most people - be reflected back on our own person, and we know that if someone did the same to us, it would be devastating.
Those who are sociopaths may lack empathy; some may lack it in a physical sense.
The brain is an organ which - if we believe evolution theory - must have evolved like any other organ. Our thoughts aren't something floating in a metaphysical realm up there, but are products of electrochemical reactions in parts of our brain that have formed partly due to what we've been using our brain for, and partly due to genetic heritage.
Here are a couple of links: