The particles that comprise this minor meteor shower were stripped off short period (6.6 year orbit) comet 21P/Giacobini-Zinner. The comet last passed through the inner solar system in July, 2005, and will next do so in February, 2012.
The radiant point in the head of Draco will be high in the northern sky during early evening, so you don’t have to wait until after midnight. Face north and you'll see Ursa Major (Big Bear), and the Big Dipper asterism. Draco stretches between Ursa Major and Polaris, the pole star, which is the end star in Ursa Minor (Little Bear), the Little Dipper asterism handle. Draco climbs higher into the sky to the left of Polaris as the night progresses. It would be best to scan this entire region of sky for Draconids.
The Draconids are fairly slow moving meteors, hitting our atmosphere at only 12.5 miles per second. Expect a maximum of no more than ten yellowish meteors per hour during peak night.