How does the Supreme Court use opinion and the intentions of lawmakers at the time to determine why and how a law was made, therefore, what does the judicial branch
do

What role does the Supreme Court play in the lawmaking process?
Although the Supreme Court may hear an appeal on any question of law provided it has jurisdiction, it usually does not hold trials. Instead, the Court's task is to interpret the meaning of a law, to decide whether a law is relevant to a particular set of facts, or to rule on how a law should be applied