You can actually see them any time the sky is dark, but as a general rule for most meteor showers, the best time is between 3am and 6am local time, that is when "overhead" (in this case toward Leo) is the direction that the earth is traveling in its orbit around the sun. Remember to dress warmly, find a comfortable dark spot with a good view of the sky and watch. Don't try to use a telescope or binoculars because they will reduce your field of view and you will miss them. Unfortunately the full moon this year is going to wash out all but the brightest meteors. Also, they don't just happen in a spot in the sky, they can occur throughout the entire sky (horizon to horizon), so don't bother to try to focus on a spot. Most will travel in a direction away from the constellation Leo (hence their name).
Also, remember that this weekend is the "peak" of the Leonids. Predictions for 2013 are for a rate of 10 - 15 meteors per hour so be patient ... it may take a while to see one. The full shower can span several weeks, so anytime in the next few days should be good.
Happy watching!
