Jurisdiction in United States?

How does jurisdiction in United States work?
Update: I am making some report from ethics, and I need to know how Jurisdiction in United States work in this way, e.g.: If some guy (lets call him Mark - civilian) accidentally kills someone. He goes to the court. Well, because I'm not from US, I would like to know how does that court calls, and what steps... show more I am making some report from ethics, and I need to know how Jurisdiction in United States work in this way, e.g.:

If some guy (lets call him Mark - civilian) accidentally kills someone. He goes to the court. Well, because I'm not from US, I would like to know how does that court calls, and what steps (courts) would he go trough, if his case would get all the way to the highest court with highest jurisdiction in US (that i also don't know how its called. I think that this is called a Subject-matter jurisdiction, and of course what is the difference between federal and state jurisdiction.
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