By being dumped in the street, going into stormwater, washing out to sea and entangling animals and fish. Turtles have been known to eat them, and also balloons, which is why I'm against releasing balloons at all.
Birds also get entangled in the bags, which catch in trees, and they starve or are taken by predators.
Animals investigate plastic bags, especially if they have food scents in them, and often get their heads trapped in the handles. They then panic, making the entrapment worse. If not found, they suffer horrific injuries and pain, and starve to death.