What is the relationship like between black and whites?
Well, it is limited. We can't say for sure what it would be like between all blacks and whites in the world of this book, only what it is between whites and this black character, who may or may not be representative.
That said, to be black in Of Mice and Men means to live in partial isolation and at risk at all times. Curley's wife can threaten Crooks quite casually, and Crooks himself "gets" to live privately—but has to live near the manure pile. He is treated with some respect and affection by some of the men, but he is definitely treated as a social inferior.
There really is no relationship. The only colored individual in the farm is Crooks. In addition to his race, he is also handicapped. He lives in the barn with the animals, and he does not socialize with the other ranch hands. The only time Crooks associates with the others is when they are playing horseshoes because he is one of the best players on the ranch. This book was written in 1939; therefore, equality among races and sexes was very limited.