I tend to read these questions literally, and you specifically asked "how" treble damages are applied.
That said, if a statute authorizes or instructs a court to impose treble damages, the court would simply take the amount of the damages that the trier of fact has awarded and multiply it by 3. So, if a jury awarded $100,000, and if a court may or must impose treble damages, it would simply increase the award to $300,000. Treble damages are a multiple of the original damages, and not in addition to the original damages.
Does that answer your question -- or were you asking about the circumstances under which treble damages are applied?