The previous writeup gives an excellent broad definition of racism, and addresses interesting scientific and philosophical issues. The word racism itself however, is quite a loaded term in American society today. When asking ourselves the question "what is racism?", we have to take into account the connotation of the word and how it is used. As in the previous writeup, this is also an America-centric discussion of racism. In other parts of the world, the concept of race is quite different, and a discussion of the difference between American and Eastern European racism would be a quite interesting topic.
Most reasonable people agree that racism is a bad thing, but many people who are accused of being racist vehemently deny having any racist thoughts. Personally I like the term prejudice to describe the unavoidable generalization and stereotyping that everyone is subjected to. I say unavoidable, because it is a consequence of the human brain's function that we generalize and experience immediate impressions of everything we see. Without this mechanism, it would be impossible to function (and survive in nature).
In the fight against racism, the exact details of what type of prejudgement are based exclusively on race is a tedious and unnecessary detail. The important thing is, of course, how racism affects people, and from that how we can personally avoid racist comments and actions.
Politically one of the most commonly discussed aspect of racism is exclusion from the American power structure. Intiatives such as Affirmative Action have been proposed and implemented in an attempt to compensate for the past injustices that were systematically inflicted on minorities in America. Minority advocates differ on their assessment effectiveness of such measures. I am not prepared to judge such a contentious issue. What I will say is that Affirmative Action alone can do little to help society permanently banish racism.
I mention this to hilight the fact that superficial rules and legislation don't solve the current problem America has with racism. After all, we already have plenty of anti-racist legislation. To really solve this problem and all the subsequent problems of cultural isolationism, people must make a concerted effort to understand each other. This starts by pushing your prejudices to the back of your mind. When you meet a person, respond to what they say, and not what you think of them based on how they look. Ask open-ended questions that don't make assumptions. Almost all racist statements boil down to either a generalization about a group of people, or an assumption about an individual based on something other than concrete knowledge about them.
For the vehement anti-racist, a high level of tolerance is necessary. Ironically, condemning racists outright is against the spirit of anti-racism. Because our personalities are shaped by our experiences, and because we all have unique experiences, judging someone else can never be logically justified. The best thing we can do to fight racism is turn a cheek to racism and prejudice which we ourselves experience. Responding in anger only increases the negative emotions and may reinforce negative attitudes. By exuding understanding and refusing to instinctively retaliate, we create the best possible outcome from a bad situation.
Finally, just as important as not reacting negatively to racism, is positive education of those near you when they propagate racist ideas. If you have a friend who is racist, the only way they will change is if they realize the negativity of what they are doing. Who else besides a friend would they actually listen to?