I ignore it in a sense that I walk away from it when I can because giving some things attention only makes it worse. And sometimes there is nothing you can do but serve by example. I know what I'm talking about. I've faced racism from whites, blacks, and Asians. In fact, I faced racism from blacks just a month ago.
Really, the best way is to just don't give a fuck. The reason why racists throw pejoratives at minorities is because they know the insults bother them. I was called a communist a few times because I'm of Chinese (actually Taiwanese) descent and I just respond with "eh" as I shrug my shoulders.