Tonight will mark the peak of the Ursid Meteor shower for 2015, thus marking the climax for the 2-week event. Every December, Earth passes through the stretch of space junk shed by Comet NAME, reaching the deepest concentration of debris tonight. According to some estimates, under ideal conditions (dark country skies), one can expect to see 10-15 meteors per hour. The reason the meteors are called Ursids is because the meteors seem to radiate from the constellation Ursa Major (the Great Bear), which contains the famous Big Dipper. The best time to view the shower is in the predawn, as Ursa Major is at its highest then.
Don't want to stay up that late? Don't worry, Ursa Major is circumpolar and is up all night. However, unless one lives out in the country, the early night hours will probably involve Ursa Majr being low in a light dome. 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.
Unfortunately, this year's Ursid peak coincides with the Full Moon. The good news: even the Moon won't be able to drown-out the brightest meteors with all its light.