While most meteor showers peak before the dawn, the Draconid meteors are generally best observed in the early evening. In the U.S. and Canada, the best viewing time would be on October 7 and 8 just after sunset.
The Draconid shower takes its name from the constellation Draco, or Dragon. The annual October event occurs when the Earth travels through dust and ice trailing from the Comet Giacobini-Zinner, according to Discovery News.
Earthsky.org offers somes tips to watch for the Draconids meteor shower :
These extremely slow-moving Draconid meteors, when traced backward, radiate from the head of Draco the Dragon, near the stars Eltanin and Rastaban. However, you don't have to locate Draco the Dragon to watch the Draconids, for these meteors fly every which way through the starry sky.
Simply find a dark, open sky away from artificial lights. Plan to spend a few hours lounging comfortably under the stars. Bring along a reclining lawn chair, have your feet point in a general north or northwest direction and look upward. If you don't know your cardinal directions, just lie down and look upward. Chill, and enjoy! You might see some meteors.