One of the reasons we often avoid thinking about what and why we believe is that we have fallen into comfortable patterns of behavior. Unfortunately these can become ruts, which are hard to climb out of. In order to get out of these we sometimes need to jar ourselves or, as one put it years ago, give ourselves a "whack on the side of the head"
From my experience here is what I have done. It is a combination of experimentation and exploration. I am at heart an experimenter - probably started when I got a chemistry set (my grandfather was a chemist) and began mixing chemicals just to see what would happen (I don't think my Mom every knew about some things that went awry in my room:)... I made a cake with some unusual subsititutions that turned out okay anyway (cornmeal for cornstarch),and later on I went through cooking experimenting phases - using some ingredient or other (like yogurt) in all sorts of dishes, with mixed results. My dad...and later my wife...have been very understanding of my urge to try all sorts of things in that area. Don't be afraid to experiment.
I am also an explorer (though not in real exotic locations). When I was younger our family would go tent camping every summer for a couple weeks. We traveled all over the western US and whenever we set up camp the first thing I wanted to do was explore the area. I was always on the hunt for something new or to see what was nearby. When my wife and I first moved to the area we are now I would often drive around and purposely get myself lost so that I would have to find my way back and would travel new roads and find new locations. It stirred my creativity and also helped sometimes when I either was truly lost or just needed an alternative way to get somewhere and now had a shortcut.
I was and am intellectually and irrepresibly curious...And I know that part of the problem today is that too many people are not. Just think about the last 8 years...do you really think our leaders cared about whether something was true or not , or whether they just took somebody else's word for it? Think how the notion of "change" has been received by many people. They fear it and don't want to change ....it takes too much thought. Fortunately many more are eager for and anticipating of much to change. Not for change sake alone, but for a return to a growing society that is ready to roll up its sleeves and work to make things better. For all.
Practical point - try to meet people who aren't like you. Different backgrounds, ethnicity, culture, race, lifestyles, bring different perspectives. It is harder to treat people as them (as opposed to us) if you know someone from that "other group". Visit sites on the web where you wouldn't normally go and try to figure out if there is something to be gained from it - at least understanding of where others are coming from.
Many years ago I read a book called "A Whack on the Side of the Head", by Roger Von Oech. He was (and is) an advocate for creative thinking and how to go about it. He used various puzzles, anecdotes, mental exercises, cartoons,and questions to help people remove mental blocks and unlock their minds. He has a website www.creativethink.com which is a good resource when you get "stuck"
Change is more than just a political slogan, or a movement, it is essential for healthy life.