In the Eastern time zone, from 5 to 6 a.m. Tuesday or just before dawn, whichever comes first at your site. (You can find when morning twilight begins by entering your location into our almanac.) Also, skywatchers in the northeastern U.S. and Atlantic Canada can try looking for a possible earlier, lesser wave of meteor activity from about 11:30 p.m. to 12:30 a.m. EST or AST.
Central time zone: From 4 to 5 a.m. Tuesday
Mountain time zone: From 3 to 4 a.m. Tuesday
Pacific time zone: From 2 to 3 a.m. Tuesday
Find a good site with an open view high to the north or east (away from the Moon), and plan to bring a reclining lawn chair and a sleeping bag for warmth. To limit lunar light pollution as much as possible, choose a site where you can observe in the shadow of a building or evergreen tree. Keep looking away from the Moon toward the darkest part of the sky.
More details about observing meteors and making scientifically useful counts can be found in several articles in the Meteors section of this Web site.
For more on this year's Leonids (including predictions for Europe, the Mideast, and West Africa) see the article "Leonids 2002: The Grand Finale" in the November Sky & Telescope, page 95.