The Leonid meteor shower peaks at 9:00 a.m., MST, on Tuesday, November 17th.
There are predictions that observers in Asia may see several hundred meteors around the peak hour. However, under normal conditions, this shower produces 15-20 meteors per hour around peak time, so the best time to look for Leonid meteors would be the pre-dawn hours of Tuesday the 17th.
The shower is named for the constellation of Leo, which contains the radiant. The radiant of the shower is the perceived origin of the meteors. You can see meteors across the sky, but if you mentally trace backward the familiar streak of light, you will notice that the paths tend to converge within the constellation of Leo.
Meteor showers are the result of the Earth passing through the debris field left behind a passing comet. The Leonids are the result of comet Tempel-Tuttle, which rounds the Sun every 33 years. We are still over 20 years from the next pass, but there is always dust and rocky debris in the path.
No telescope or binoculars are needed. Just dress warm, and watch the skies for Leonid meteors.