If you were raised in an almost solely single-race environment, your amygdala will decide within tenths of a second when you meet a person of another race that he is a Them, not an Us. The amygdala is an ancient part of the brain that is correlated with experiencing fear and anxiety. So what do we do about the fact that most of us were hard-wired in childhood toward racism (not by bad experience, but by lack of early exposure)? Prevention is, of course, preferable: make sure your toddler is raised with inter-racial exposure.
If it's too late for that, you can over-ride that innate reaction by harnessing a stronger one - the love-hate relationships in sports. If you love Chicago and hate Green Bay, carry around Chicago caps and give them to people you meet of another race. You will start immediately feeling less fear and anxiety and more of an Us than Them relationship - honest.
However, for most of us, it is simply a matter of being aware that our immediate innate feelings are false and being willing to treat everyone as an Us until they prove otherwise.
"We cannot solve our problems with the same thinking we used when we created them." ― Albert Einstein
"Get your facts first, then you can distort them as you please." ― Mark Twain