Modern darts are made from Brass (least expensive), Nickel/Silver (Nickel and Tin alloy) and Tungsten Darts (the most durable and expensive).

The shafts are manufactured from composite materials (plastic bases, combined with aluminum or other metal alloy tops that hold the flight) or solid Aluminum.

Flights (the fins/wings) act as stabilizers and are available as various types:

• Hard flights (“Poly Flights”) are made of a stiff polyester plastic;
• Nylon flights, as the name implies, are manufactured of ripstop nylon fabric, and are by far the most durable type of flight;
• Soft flights are not so popular anymore and are made of a flexible plastic sheet folded into shape.

You can read more at Rick Osgood’s excellent website. Below is a video that illustrates how these darts are made.