A reclining lawn chair will make it easier to watch the sky. Lesser numbers of Leonids will be visible for about a week around the date of the peak. This stream of particles is thickest near the comet itself, and Comet Tempel-Tuttle has been spotted coming back into the inner solar system. It will be closest to the sun in February 1998. It is not a bright comet, but in January it will be visible to those with telescopes.
Most meteor showers happen when Earth crosses the orbit of a comet.
The meteors are particles of dust released from a comet's nucleus and left behind in space as the comet gets closer to the sun. The particles follow the comet, however, all drifting along in the same orbit around the sun. When Earth plows through this stream of particles, the particles burn up almost instantly by friction with Earth's atmosphere. The resulting heat momentarily causes the air molecules around the dust particle to glow brightly, and we see a meteor. If you would like to do more than just watch the Leonid meteors, you can participate in an international effort to study the Leonid shower by recording the meteors that you see and reporting your results to the International Meteor Organization.