You can't. Someone with standing (someone who is personally, negatively and significantly impacted) would have to initiate a new case that challenges the established precedent sufficiently to warrant reconsideration of the matter. The party bringing the case would have to lose at both the trial and intermediate appellate level (or hope the opposing party has sufficient interest in pursuing an appeal if they lose) before the case can be petitioned to the US Supreme Court.
In the 2008-2009 Term, the Court received 7,738 petitions for writ of certiorari from people who wanted their cases reviewed. Of these, the Court can only choose about 150 cases for disposition; only about half the cases selected are scheduled for oral argument and receive full written opinions. Cases are selected on the basis of topicality, national significance, and constitutional issues raised. They may be willing to take a second look at a precedent, or may decide the law is settled - at least for the moment.
Even if the justices grant certiorari on a case involving an established precedent, and even if the Court agrees that a particular application should be handled differently, they may make a narrow ruling creates an exception while leaving the earlier decision substantially intact. This outcome is more common than one that completely overturns a prior decision.
In any event, there is no way to compel the Supreme Court to review any particular case. The Court has full discretion over cases heard under appellate jurisdiction. Statistically, the likelihood of having the case rejected is 98-99%.
For more information, see Related Questions, below.
By issuing a judicial review.
Judicial Review
Marbury vs. Madison
per curiam
Centiorari or Writ of Centiorari
the principle of judicial review was established
Marbury vs Madison established the principle of "judicial review."Judicial review says the Supreme Court can decide on whether laws passed by Congress and signed by the President are constitutional.
It was a concept of judicial review. In other words the supreme court have the authority to review other branches of court and decide whether or not the cases are unconstitutional.
Marbury vs. Madison
If you've applied for, college, and you see that a departmental status review is required, it simply means that a decision on your application has not been made yet.
Supreme Court Review was created in 1960.
ALL lower courts, both state and federal, can be reviewed by the Supreme Court. Every court in the nation is subordinate to the US Supreme Court.