Why is Crooks discriminated against, and what are some examples?

Crooks is discriminated against because he is a black man. In the 1930s, African Americans and Chinese immigrants had few rights in California, the setting of Of Mice and Men.
It is interesting that in the description of Crooks's quarters in the harness room, he has "scattered about the floor" several personal possessions, among which is "a mauled copy of the California civil code for 1905." This book is apparently an old manual that Crooks has had since his youth. It seems he has studied it often, since it has been held a great deal. It would seem, then, that Crooks has educated himself in the laws of the state so that he knows what rights he has and what rights he is denied.
Earlier in the narrative, George Milton speaks of how the disenfranchised men of his time who move from job to job alone become mean. Such meanness was displayed by the ranch workers earlier in the narrative when Candy told of the time that the boss allowed Crooks to go into the bunkhouse at Christmas and the men were given a gallon of whisky. Without any sympathy for Crooks, old Candy tells George and Lennie,

Little skinner name of Smitty took after the n****r. Done pretty good, too. The guys wouldn't let him use his feet, so the n****r got him.  If he coulda used his feet, Smitty says he woulda killed the n*****r. After that the guys went into Soledad and raised hell. (Section 2)

Later, as George plays cards, he hears a voice outside calling "Stable Buck." He then hears the voice say, "Where the hell is that G...d...n****r?" Apparently, there is something in man's nature that causes him to want to feel superior to someone else, no matter how low he may be. This desire to demean someone, along with racial bias, is likely the reason why Crooks is the victim of insults and discrimination.