Key concepts in general federal law, at all court levels, include standing and the Case or Controversy Requirement. These apply as strongly to constitutional cases as to any others, and often a seemingly "civil rights related issue is rejected by the courts for these reasons. They flow from Article III, Section 2 of the United States Constitution. Standing means that a person raising a constitutional issue must be someone who, if his or her assertion is correct, will personally suffer an infringement of his or her rights if the court does not intervene. This means that, except in unusual circumstances (see class action), one cannot sue on behalf of another. The Case or Controversy requirement means that there must be at least two adversarial parties and an actual problem between them. The effect is that federal courts in the United States do not issue advisory opinions or rule on hypotheticals. (But see: Declaratory judgment).
To these two concepts, constitutional law adds the state action requirement. Simply put, a private citizen cannot violate another private citizen's constitutional rights. A case does not become a constitutional issue unless one party can show that a local, state, or federal government agency or official was involved. For example, if a private citizen invades another citizen's house, the first citizen is liable to the second one in a lawsuit for trespass; on the other hand, if a policeman invades a citizen's home without a warrant or probable cause, the police agency can be found liable for violating the citizen's constitutional rights.
The first example is merely a violation of the legal right to privacy; the second is a violation of the constitution's prohibition on unreasonable searches and seizures. (Note here: Some cases which the Supreme Court of the United States accepts and decides involve constitutional rights; others involve the interpretation of legal rights.)
Generally, when a case has cleared the hurdles of Standing, Case or Controversy and State Action, it will be heard by a trial court. The non-governmental party may raise claims or defenses relating to alleged constitutional violations by the government. If the non-governmental party loses, the constitutional issue may form part of the appeal. Eventually, a petition for certiorari may be sent to the Supreme Court. If the Supreme Court accepts the case, it will receive written briefs from each side (and any amici curiae or friends of the court--usually third parties with some expertise to bear on the subject) and schedule oral arguments. The justices will closely question both parties. When the Court renders its decision, it will generally do so in a single opinion for the majority and one or more dissenting opinions. Each opinion sets forth the facts, prior decisions, and legal reasoning behind the position taken. The majority opinion constitutes binding precedent on all lower courts; when faced with very similar facts, they are bound to apply the same reasoning or face reversal of their decision by a higher court.