My cat got his paw crushed by a car, and we don't have money to get it fixed. what should I do?

If you cannot afford the vet, I would say thinking about a no kill shelter and putting the animal's welfare above your own needs is a commendable thing to do. Make very sure that it is a no kill shelter, rather avoid the SPCA, who say they are a no kill shelter, but they do put animals to sleep who are not adopted, every week.