They follow Jewish law, but Jewish law often takes the local law into account. For example, Jewish law often considers common business practice, which in the United States is often a product of American law. If someone enters into a contract that is binding according to American law, then they are generally bound by Jewish law as well, because the business community considers such contracts binding.
Also, there is a principle in Jewish law called “Dina D’malchusa Dina,” literally, “the law of the government is the law.” The exact parameters are somewhat complex, but this means that Jewish law recognizes many secular laws. Bankruptcy laws are often a good example.