This page describes how product liability works in the world of Snowcrash.
All reputable companies which produce toys, consumer goods, etc. generally contribute to an insurance pool. People who claim injuries from such things can file claims which are handled with binding arbitration. The process can take years, and there are no punative damages awarded.
This is the method most people get stuck with.
This is the method favored by the rich, and lawyers.
The final option is to talk to the local media, hope you are photogenic enough to make a good impression, and then hire a lawyer to negotiate with the toy's manufactuer.
This is the method favored by people who want to be on TV.