It usually goes something like this: originating court, then the court of appeals, then the supreme court.

its a long process. depending in which circuit it starts in, it could potentially go through like 6 different courts. but its an appeals process. so you have to appeal your case up to the supreme court, they issue a writ of certiorari to get information regarding your case, then they decide if they want to hear it or not, and unless your case deals with a constitutional issue, then it most likely wont reach the supreme court, in which case, the last courts ruling stands

That depends on several factors. Note: I assume you mean the U.S. Supreme Court. First, there are a few disputes in which the Supreme Court has original jurisdiction (i.e. the case starts in the Supreme Court), but I am sure you are not referring to this. Second, if your case starts in a federal court, then you would get to the Supreme Court by appealing your decision to the appellate court (i.e. circuit court), and then appealing to the Supreme Court if you think the result was erroneous. Third, if your case originates in state court, then you can only appeal to the Supreme Court if: (1) your claim deals with a federal question, and (2) you have a final judgment from the highest court in the state. In most states this means you went to trial, you appealed to the intermediary appeals court, you appealed to the state’s highest court, and then you can appeal to the Supreme Court. Some states don’t have an intermediary court, so in those states you would skip that step. Finally, it should be noted that cases are accepted by the Supreme Court by writ of certiorari. Unlike most appellate courts in which the court must accept all cases, the Supreme Court gets to choose which cases it will take.