You have to start when kids are young, and build in them strong self-esteem, acceptance for multiculturalism, and the grit to stand against racial differences.
Racism exists. No matter how much ever you try to protect your child, your kid at one point or the other is going to have a brush with racism. There can be two scenarios: in the first, your child may become the victim, and in the second, he could be the one to pass a racist comment. You just have to be ready with the tools to combat this problem so that they can deal with racism tactfully, and more importantly, correctly.
The foremost thing that you need to do is... keep all your hesitation aside. In the beginning, you may feel awkward to confront your child, but you have to be firm and honest. You have to make him realize that the world we live in is made up of all sorts of people and skin colors. It adds variety to the world. You should make him understand the importance of tolerance. And if you are finally confronted with a question, think of it as an opportunity to get a glimpse of how he perceives the world.
Few Hints to Start the Conversation About Racism
Bring Up the Topic Confidently
Most of the time, parents are afraid of bringing up the topic of racism with kids, because, in the times when they grew up, discussing racism was taboo. I completely understand this hesitant attitude, but with the advent of the Internet and smartphones, the world has turned into one global village, and kids are abreast with all the latest information. Therefore, they keep hearing about racism all the time, and you have to simply accept it.
My advice would be to be confident, and initiate the talk. Don't think that talking about racism will make them more or less racist. If you are a multiracial family, then you can start by showing your kid photos of your family members, and telling them how people from different ethnic backgrounds have and are living together happily.
Grab the Teachable Moments
If you are with your kid, and the topic of racism comes up on the TV, or if they come across the topic in a textbook of history, just grab that moment and tell the child more about racism. Explain that even though skin color is different, we all belong to one human race. If the child directly poses a question or makes a racist comment before you say anything, then nothing like it; you have the perfect moment waiting to be taken.
But, you don't have to overreact; just be calm, and ask the reason behind the comment. Many a time, it happens that the child may just be repeating what he has heard in school or on TV, and means no harm. But, in such an instance, if you make a hue and cry about it, and give undue importance to the topic, then the child may think that such topics are serious and intent.
Wisdom Imparted Should be Age-Appropriate
If your kid is too small to understand racism in words, then maybe you could demonstrate a small experiment. You can bring two eggs from the market, one white-colored and other brown-colored. You can break the eggs and show it to the kid that, inside, both the eggs contain the same content. Likewise, it doesn't matter what the color of the skin of a person is, everyone is the same from inside, and have equal rights to live with dignity.
For the little older kids who can understand the meaning of racism in abstract terms, you can play with words. If your kid is above 8 years of age, and can read a book with proper understanding, then you can give him 'Let's Talk About Race'
by Julius Lester. One more way of inculcating the spirit of anti-racism in children, is to encourage them to get involved in charities or organizations that fight racism.
Try to Promote Multiculturalism
You should emphasize on the importance of multiculturalism. You need to tell your kid that people of different races are the same type of person inside. It's just that they have just grown up in a different environment, and so they behave and speak differently. In the meanwhile, you could expose your child to various cultures by giving him multicultural books to read, or asking him to try to make friends with kids from different cultures. You can also ask him to participate in the festivals of other cultures.
Be a Role Model for Your Kid
If you figure out that your kid's school is the breeding ground for racist behavior, then you should visit the school and talk to the teachers about it. If talking to them doesn't help, maybe you should escalate the issue further to the principal. You can also talk to the parents of other transracial kids about the issue. See if their kids are facing a similar problem. When your kid sees you put your foot down and stand up for the issue, he will realize that racism isn't a nice thing, and should be avoided.
At home, you need to set an example by demonstrating to your kids that you have friends from all backgrounds. You can show that you enjoy learning foreign languages, you like to listen to music from other cultures, and also admire their art. It is only then that your kid will follow your footsteps.
So, if your child has hurt someone by passing a rude comment on the color of their skin or hair, then you have to encourage him to apologize and not repeat the mistake. I can only say that, make your child understand that no race or culture is bad or inferior, it's just different.