Crookshanks is half Kneazle, so he has some magical prowess as a feline. And I think because of that, Crookshanks knew that Sirius wasn't a real dog, so he trusted Sirius. And Sirius told Crookshanks all of his woes, and all of the things he was trying to do. And Crookshanks realized the truth of the statements, so he helped Sirius.