There are both civil actions for fraud, which have certain elements, procedural features, and standards of proof, and crimes described as fraud, which have different elements, procedural features, and standards of proof.
In a suit for common law fraud, one must prove each of the following elements of the claim by a preponderance of the evidence at trial with admissible evidence (with subtle variation from state to state) that there was a (1) misrepresentation made by the defendant to the plaintiff, (2) regarding a material fact, (3) upon which the plaintiff was intended to rely, and (4) upon which the plaintiff actually did justifiably rely, and (5) that reliance caused the plaintiff to suffer (6) economic damages in an amount proven at trial.
A plaintiff does this by filing a lawsuit (or a counterclaim or an affirmative defense, as the case may be), setting forth the facts giving rise to the claim, in a court with jurisdiction over the claim, and going through the process of the rules of civil procedure (which differ a great deal from the rules for criminal cases). The complaint initiating a fraud case is held to a higher standard than an ordinary complaint initiating a lawsuit and must be "pleaded with particularity" that sets forth the basis of the alleged fraud claim in greater detail than would be required for other kinds of lawsuits.
The same acts can give rise to both civil lawsuits, and criminal charges.
Furthermore, in some cases, fraud can be asserted as a defense to someone else's civil claims (e.g. breach of contract), rather than as an affirmative cause of action seeking damages of its own.
Even the subset of cases where fraud is an affirmative defense has fine gradations. Certain kinds of fraud will make an act "void ab initio" (i.e. preventing an legally relevant act from ever having taken place), while other kinds of fraud merely render a legal action "voidable" (i.e. subject to being invalidated if and only if someone affected by the fraud complains and raises the matter in a legal forum).
Also, yet another body of law applies to fraud, not in the underlying conduct that is the basis for a civil action or criminal prosecution, but in the court process itself. This implicates rules related to discovery sanctions, rules related to fraudulent court documents, ethical rules for lawyers that can lead to disbarment, contempt of court sanctions, rules for setting aside legal judgments and convictions based upon fraud, and criminal perjury prosecutions, to provide some of the main examples.