After a defendant is found guilty in federal court, he may appeal the verdict, the sentence imposed by the court, or both. The first step is to file a Notice of Appeal.
The appeal will first be heard by a panel of three judges. The defendant submits a written brief explaining what mistakes were made by the trial court. The government then has the opportunity to submit a brief in reply, explaining that no mistakes were made or that, if they were, they were harmless error that did not affect the final verdict. The Court of Appeals will usually decide the case on the briefs. However, sometimes, the court will ask the parties to present oral arguments. In that case, each side has fifteen minutes to explain why he should win. The judges may interrupt to ask questions. Some time later, the Court will issue a decision. If the defendant disagrees with the Court's conclusion, he can seek rehearing before the full court. The full Court may decline to hear the case.
Finally, the defendant can file a petition for writ of certiorari with the Supreme Court of the United States. The Court declines the vast majority of these requests without opinion. A refusal to review the case is not adjudication on the merits. If the Court accepts the case, each party will submit a brief, and then appear before the court for oral arguments. Again, the court may interrupt to ask questions. Some time after the argument, the Court will issue a written decision. The defendant cannot appeal a decision by the Supreme Court of the United States.