How does a court decide?

What is the case with Beit Hillel and Beit Shammai? It turns out that interpretation doesn’t really matter, it’s the quantity. That is, a court of law can seemingly draw an opinion or even err in its thinking, but its words are words of Torah. And in fact, who determines who is a court of law? A bunch of ignorant Torah-observant people can call themselves a court of law and establish baseless decrees and regulations that seem reasonable to them and are supposedly Torah. So how does this actually work?