How do we pick federal judges?
The President nominates them and the Senate confirms them. This is for all federal judges: District Court, Circuit Court, Supreme Court, International Trade Court, etc. These judges serve for life as long as they exhibit “good behavior”. Like the president, their salaries can’t increase/decrease while in office. They can also be impeached.
What cases do they decide?
Stuff around the Constitution or involving ambassadors, ministers, and consuls. Cases involving the high seas (seems like a lot was happening out on ocean back in the day). Cases where the U.S. is prosecuting or defending. Controversies between two or more states, or a state and citizens of another state, or between citizens in two different states. Look, if the case isn’t completely contained within a state, it becomes a federal case. Also cases with ambassadors, ministers, consuls, and states – those cases start in the Supreme Court (rather than get appealed to it). There’s also a ton about treason; but in short, you need 2 witnesses to be convicted of it. In short, try not to commit treason.
How many federal courts are there?
This isn’t specifically in the Constitution, but in the federal government there’s 1 Supreme Court with 9 justices, 13 Circuit (a.k.a. Appellate) Courts with 179 judges, 94 District Courts with 673 judges, and 1 International Trade with 9 judges. The numbers change over time, but that’s where we are right now.
Just remember that federal judges are nominated by the President, confirmed by the Senate, and serve for live. Also, don’t commit treason – it’d be a huge headache.