Since the Judiciary Act of 1925, virtually all cases before the United States Supreme Court get there by petition for writ of certiorari, rather than an appeal "of right". The difference is that the Court may refuse to grant the writ of certiorari. In fact, given the enormous number of appeals to the Supreme Court these days, the writ is rarely granted.
It takes the votes of four (4) of the nine (9) Justices to obtain the writ. Over 7,000 petitions for writ of certiorari are filed in the Supreme Court each year, but the Court only reviews about 100 cases (and decides 40-50 more summarily, without hearing argument or issuing a formal opinion).
Cases usually get to the Supreme Court either from the next highest appeals court in the federal system (a federal "Circuit" Court of Appeals) or from the highest appeals court of one of the States. Either way, cases do not come directly from a trial court. At least one court of appeals --sometimes two layers of appeals courts, if the matter came up through a state judiciary-- has already reviewed the matters. Facts are not up for debate: the party that won at trial is presumed to have presented the truth. Routine legal matters such as judges’ purported mistakes have already been dealt with. All that makes it to the attention of the Supreme Court are the most important and generally applicable issues of law.
Even though it is only one small step towards a decision, the announcement that the Supreme Court has granted “cert” is news because it means an important issue will be decided --one way or the other.
See "About the Supreme Court", www.supremecourtus.gov.
A list of the cases where cert has been granted can be obtained fromm the Supreme Court’s website at http://www.supremecourtus.gov/orders/orders.html: click on the link to “Granted/Noted Cases List” for a .pdf format document.