It depends on how the crash happened, but the key difference from an ordinary crash is that there may be no at-fault human driver in the usual sense. With a fully autonomous vehicle, responsibility can shift to the company operating the vehicle — like a robotaxi service — the manufacturer, or the maker of the self-driving software or sensors.
When the vehicle's own systems caused the crash, product-liability principles can apply to the maker, and negligence theories can apply to the company running the vehicle. Often more than one party is involved, and identifying every one is central to these cases. If another human driver was actually at fault, that driver can be responsible in the usual way.
Because the field is new, these claims are built carefully around the vehicle's extensive data and expert analysis. Preserving that data quickly is one of the most important early steps, since it can show exactly what the vehicle detected and decided.