I believe the car accident I was in was caused by defective brakes. How do I file a claim?

You should retain a personal injury attorney with products liability litigation expertise.  The dealer is most likely a candidate for negligence complaint for failing to inspect or discover the brake system defects.   However, the state courts are split on whether dealers in used goods should be subject to strict liability; unfortunately for you, holding them strictly liable appears to be a minority position.  If your state permits you to pursue the auctioneer – a “downstream” seller of the vehicle – regardless of what steps it took in handling the car, you can make a strict liability claim ifall three of the following conditions exist: the product had an “unreasonably dangerous” defect that injured you as a user or consumer of the product, and the defect can come into existence either in the design of the product, during manufacture, or during handling or shipment; the defect caused an injury while the product was being used in a way that it was intended to be used; and the product had not been substantially changed from the condition in which it was originally sold.  “Substantially” means in a way that affects how the product performs.