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To see the most meteors, go out after midnight and watch in the general direction of the constellation Perseus - and be sure that you're on the right side of your town so that Perseus is in the darkest part of the sky. Going out after midnight allows you to look into the direction of the Earth's orbit, kind of like looking out the windshield of your car in the rain: You see more raindrops heading into the rain than away from it. If you have a dark sky, you could see up to 60 meteors/hour. Note that you can see meteors for several days before and after the peak, just not quite at that rate.
Thanks to bellanorth's post for the reminder. (Read my reminiscence about watching a show many years ago on her LJ, too.)
EDIT: Go here to see a map of the sky on Saturday night. You'll see that Perseus is in the northern sky, right near Cassiopeia (the big W not far from the Big Dipper).