To see the Leonids, find a dark location and let your eyes adapt for at least 10-15 minutes. Dress warmly and relax on a blanket or lawn chair, looking overhead or somewhat toward the east. The 'raidant' of the meteor shower is in the constellation Leo which rises high in the east after midnight, and the meteors will appear to emanate from that spot, but will shoot all over the entire sky, so most important is to have a view of as much of the sky as possible. City dwellers should find the darkest possible spot. In my own backyard, I place myself in a dark area where the local streetlights are shielded from view, allowing my eyes to adapt and see fainter meteors.
Stay warm, and enjoy the show. Here are some additional resources:
Space.com article about the Leonids.
Earthsky.org article about the Leonids.
Image courtesy howstuffworks.com.