On the night of Tuesday/Wednesday August 11/12, the annual Perseid meteor shower will peak. If you find a dark spot and go out after midnight, you should see up to 60 or so meteors zinging across the sky per hour. This year is not as great as previous years, since the Moon will be up almost all night and washing out the sky somewhat, but if you make the effort I'm sure you'll see quite a few shooting stars.
For the 2007 Perseids I wrote up a post called 12 Things You Need To Watch the Perseid Meteors, and nothing really important has changed since then, so reading that will give you a good guide on what you need to do if you want to watch the show. One thing that has changed since then, though, is the advent of Twitter! It has a lot of uses, including those astronomical ...