The Leonid meteor shower will peak this week on the night of the 16th, and last through the morning of the 18th. It is one of the brightest meteor showers that we see all year as the Earth passes through the dust and small debris from the Comet Tempel-Tuttle. The unfortunate thing about this year is that the Moon will be full Saturday and Sunday night, but the good news is that some of these meteors are so bright that you might be able to see some of the brightest ones!
At the best peak you could see around 15-20 meteors per hour, but if you really want to have a chance to see them you will need to get out from outside city limits and head to the country!
The place you will need to look is to the eastern skies after midnight starting tonight and keep looking all the way until next Wednesday. Look towards the constellation Leo where the name Leonid originates. See how many you can count and we can talk about it on my facebook page!