Dog vomited half-digested food, then white foam, now clear water with foam

From your description, the dog first vomited undigested food, then white foam, mainly from eating too fast, too much, or ingesting foreign objects. In this case, withhold food and give pet probiotics, watching for improvement. If it persists, consider gastritis, pancreatitis, liver disease, intestinal blockage, parvovirus, or coronavirus, and see a vet.