Tonight will mark the peak of the Leonid Meteor shower for 2015, thus marking the climax for the 2-week event. Every October, Earth passes through the stretch of space junk shed by Comet Tempel-Tuttle, reaching the deepest concentration of debris tonight. According to some estimates, under ideal conditions (dark country skies), one can expect to see 20-30 meteors per hour. The reason the meteors are called Leonids is because the meteors seem to radiate from the constellation Leo. The best time to view the shower is in the predawn hours, as Leo is at its highest then.
To improve odds of seeing meteors, travel out of the city and to the country if you can. In the suburbs, just going from the front to back yard can make a dramatic difference as this will eliminate glare from those pesky street/house lights to a large extent.
Fortunately, this year's Leonid peak coincides with the First Quarter Moon, which means that nature's night light will be a non-issue as it will have long since set by the time the predawn hours arrive.