The "Rights of Nature" idea reaches all the way back to 1972 (two years after the first Earth Day) when Christopher Stone, a University of Southern California law professor, suggested in his essay Should Trees Have Standing? that they should. He was one of the first Western legal scholars to contemplate nature’s ability to take part in lawsuits.
Rights-of-nature laws often work by appointing a guardian to advocate for a particular ecosystem or natural feature, much like a parent represents a child’s interests in court (Guardian ad Litem). The guardian can sue on the ecosystem’s behalf. If the ecosystem is awarded damages, the money might go into a trust dedicated to funding its restoration.
I may not be a lawyer to sue on behalf of Gaia, but I can still guard her interests by any means necessary. And you can, too.