How are cases presented to Supreme Court Justices?

That depends on what you mean by "presented."

Cases are typically appealed to the US Supreme Court on a

petition for a writ of certiorari, which includes a legal

brief prepared by the attorney or attorneys for the petitioner

(similar to a plaintiff). The respondent(s)' attorney(s) may oppose

the petition with their own brief.

If the Court grants certiorari, the case may be scheduled for

oral argument, allowing each side 30 minutes to explain to

the justices why their client should prevail. During oral argument,

the justices ask questions about the case or relevant precedents

and points of law (although the justices are often better prepared

than the attorneys, already know the answers to the questions, and

may have already decided how they are going to vote after case

conference).

-Hops