At 9:40pm CST, the Leonids will reach their peak in the eastern sky. Just look towards the constellation Leo, and you could see as many as 20 meteors per hour.
The Moon will just be sneaking off the horizon, so it's light may wash out some of the display. However, if you are in an open field or out on the beach, you still could have a pretty good show, if you show some patience.
The Leonids are dust leftovers from the comet Tempel-Tuttle. Earth's orbit around the Sun carries us through the comet's debris field.
The next meteor show will be the Geminids in December.