You need not be a whiz at critical thinking in order to help your children improve at it. Two of the most important things are for them to be reflective and open minded. You can encourage reflection and open-mindedness by asking them a few judiciously timed questions when a decision about what to believe or do is in the offing, or has been made. For example, here are some things you might say: “Have you thought about the alternatives?” “Why do(or believe) that?””
Is this a good source of information?””Stop and think about it.” These questions are in line with the RRA strategy: Reflect, seek Reasons, and compare Alternatives (described at the beginning of  Twenty-One Strategies and Tactics for Teaching Critical Thinking). The RRA strategy, if used with discretion, is useful for all people, including young children. The way you use it depends on the situation. You must think critically about that !

As well as gullibility and lack of reflection, cynicism and skepticism are dangers as well. So do not promote total negativity either.Your being an example of reflection and open-mindedness would help as well. But do not expect immediate results with your children. It takes most people lots of practice in a variety of situations to become good critical thinkers.

At a somewhat more detailed level, some textbooks that you might consult in order to decide what to say, question, and encourage are listed on the web site of Association for Informal Logic and Critical Thinking (AILACT). To get more ideas for teaching critical thinking, see Twenty-One Strategies and Tactics for Teaching Critical Thinking. Although the first three focus on the suggestions in the first paragraph above, the others can be very helpful in pursuit of this RRA strategy.

My textbook in the AILACT list is not a textbook for beginners. It is more appropriate for critical thinking teachers, or those willing to take a full year college course in it, but you might find it of help if you have the time and interest.

A study of the rest of the web site you are now viewing would be helpful as well. For example, you might be interested in self-teaching and critical thinking assessment.

In two successive issues of the journal Inquiry (2011), I have a two-part history of the critical thinking movement over the years, and of my work in it.

Your suggestions are welcome.