The most important thing to remember when thinking about atheists is that atheist does not equal anarchist. Atheists believe in order and morality.
Now theists will argue that there is no source of an atheist's morality because there is no higher order instructing these morals upon us. While we don't believe in a higher source, we believe in order because without order, humanity is susceptable to chaos and self-destruction. Our principles are really based on the cliche, "Do to others as you would do to yourself." This is the atheist's banner. So that means if you're an atheist, you believe stealing, lying, cheating is all wrong because you don't want it happening to you, therefore you don't do it to others.
Of course, this is simple to understand. When it comes to the realms of other moralities such as abortion, slavery, and human rights lines can become blurred. Christianity defended slavery in the South. Christianity defended the Crusades. You will rarely find an atheist that believes that any such thing is acceptable. Christians believe Jesus died for them on the cross and Jesus said not to accumulate wealth. How many Christians actually don't accumulate wealth and share it. So morals and religion, in this discussion Christianity, are hardly proportional.
Being an atheist, has no bearing on my opinion of abortion. I'm against it, however, I am not against the right for another woman to choose. It is their body. Why am I against unnecessary abortions, aka abortions without special circumstances? I feel that it is wrong to kill something that will certainly become a human being. I don't need a god to know that killing is wrong. Its rather obvious that it is wrong.
Now the key to atheistic belief. The stronghold of our morality is also our lack of a belief in an afterlife. This will be attacked by some and say we can do whatever we want without consequence. However, this goes against the order of life we want. In reality, with no belief in the afterlife, we feel that the value of life is on a much higher scale of value than that of any theist. Therefore to kill someone would be the ultimate crime for us. To abuse a person, to make their existence hell is a crime because there is nothing else. All you have is life, so we want life to be as pleasent as possible. Theists believe that heaven will be worth the suffering. We don't believe in such a reward. Therefore, life on Earth must be filled with moral righteousness because there is nothing else.
If you need anymore details, please feel free to ask.