Summarize this article:

Pull your hand slightly back as you throw. Use your hand, wrist, and elbow for speed. Keep your shoulder still for support. Place more weight on your front foot as you throw the dart.  Do not lean or sway to the side. Keep your body still and straight. Only your arm should be moving when you throw the dart. Your elbow may raise up slightly when you throw the dart. This is okay, as it may move upward due to the force of your throw. Let your wrist snap forward as you release the dart. Make sure your wrist does not snap downward, as this will cause the dart to fly downward. The wrist snap is often done by professional players to increase the acceleration of the dart. It can also result in a more accurate and consistent throw. Once you have released the dart, let your arm continue in a throwing motion so your fingers are pointing towards your target, or down at the floor. Allow your arm to hover in the air for a moment before you drop it down. This will help you maintain good form at the end of your throw.

Summary:
Throw the dart with your hand and wrist. Snap your wrist as you release the dart. Follow through at the end of the throw.