How do anti-discrimination laws work in the United States?

So for example, if the owner of an apartment building flat out said, you can't live here because you are whatever nationality, ethnicity or skin color.

What would happen?

Could the courts force the owner to let you live there?

Would the owner have to pay a fine or go to jail?
Update: "You can sue the landlord for discrimination and file a complaint."
But what will come about from that is my question? Will the court force the landlord to accept you? Will he or she have to give you a certain some of money? Would the landlord go to jail?
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