The annual Leonid Meteor Shower will peak tonight. The Leonids are not the most impressive show of the year, but the viewing conditions will be ideal with no bright Moon washing out the meteors. You can expect 10-20 meteors per hour, which is a little over twice the rate for the normal sporadic rate that occurs each night.
Go out between midnight and dawn and find a wide view in the darkest place available. Look just north of east until you see Leo, a hook-shaped pattern of stars. This is the radiant, the point in the sky where the meteors seem to be coming from.
If you miss the show tonight, you can try Saturday night since the rate will be close to Friday night's rate.
Finally, plan ahead to watch the Geminid shower in December. That will deliver about ten times what the Leonids produce.