In the United States, law is enacted by elected officials be they city, county, state or national. If a law is challanged by someone charged with violating it, it can go through the court system and eventually the US Supreme Court.
Elective legislatures are charged with developing the laws. Elected executives are charged with enacting or vetoing the legislation creating the law by signature. Judges, some elected and some not depending on jurisdiction, are charged with intrepreting the law.
The US legal system is based on English common law philosophically, but the administration is different. The foundation is our Constitution which assigns the areas and limits of responsibility in the creation of our laws.
Our courts, especially at the federal level, are divided between "activists" and "strict constructionists". Activists are accused of "making new law" by intrepreting laws as extending into areas not otherwise originally intended. Strict constructionists attempt to abide by the letter and original intent of law based on the Constitution. In short, this constant tug-of-war makes the legal system in America a living, adapting entity.
No American judge at any level has the authority to author "common" law as in Australia.