Parents raising their children without gods or religion should teach them how to be skeptical, how to engage in critical thinking, and how to fairly apply the standards of reason and skepticism to religious and paranormal claims which they might encounter. They should also learn how to do so without necessarily attacking those who hold these beliefs. Sometimes there will be people who should be criticized personally, but it should not be the first or only tactic adopted.
Children need to learn to be skeptical because they will encounter a large number of claims, ideas, and opinions throughout their lives and they can't assume that they are all true. On the contrary, most are probably false or at least partially false. It would be wrong to simply accept all these claims at face value, and a consistent, reasoned skepticism is a good way to separate the wheat from the chaff. The scientific method, in turn, is the best way for investigating claims, testing whether they are true or not.
Teaching skepticism and science to children isn't as easy as teaching a subject like arithmetic or history. There aren't any lists to memorize or procedures that can simply be repeated the same way every time. Skepticism, at least, can be more about attitude and perspective rather than mere knowledge. In effect, what children need to do is learn skeptical, critical, and scientific habits a way of looking at claims and reasoning through the ideas they hear about. Habits like this have to be developed over time and inculcated in small steps that grow gradually.
Fortunately for atheist parents, kids are natural skeptics and questioners indeed, their penchant for asking questions about everything has driven more than one parent to distraction. However annoying this might get at times, a child's desire to question everything should be encouraged rather than discouraged. While a parent might want to appear to know everything, it's also important to be able to say "I don't know" to some of the questions.
As a matter of fact, saying "I don't know" allows parents to teach their children not only that no one knows everything, but also that it isn't necessary to know all the answers. Here parents can teach their children how to use various resources such as dictionaries and encyclopedias to research questions in order to arrive at their own answers.
This may in fact be one of the most important lessons for parents teaching their children to be skeptical and scientific in their approach to life. It's okay not to know an answer, but it's not okay to pretend you know the answer or to make up an answer simply because it fits in with your preconceptions. It's okay to ask questions and want to know more, but it's not okay to assume that you already know enough and having nothing new to learn or understand about the world. These are the attitudes necessary for anyone to have before they can even think about exercising skepticism and critical thinking or applying scientific methods to learning about the world.
By teaching kids about how to research questions and learn answers, whether in books or through their own experiments, you will also be teaching them many of the basics of skepticism, critical thinking, and science. Being skeptical and critical means being active and taking responsibility for what you believe, so teaching children to take responsibility for researching the answers to their questions means teaching them not to simply rely on what authority figures like you tell them. You'll be teaching them to be more independent than those who accept what they are told and move on without further comment or question.