What a great time to ask about finding extrasolar planets -- planets orbiting stars outside our solar system!
On Friday, NASA just launch a special robotic spacecraft - the Kepler Mission (http://www.nasa.gov/mission_pages/kepler) - which will look for planets around other stars. It finds them by monitoring the light from the star and watching for a small dip in the brightness that is caused by the planet passing in front of the star, blocking out some of the light. And there's another European spacecraft up there searching, too. It is named Corot.
Two other techniques make use of the fact that in any planetary system, the star and all the planets actual orbit around the center of mass of the whole system. So if a star has a really heavy planet - such as Jupiter - the star actually oribits around the "center of mass" location. We can detect this little "wobble" in the stars motion.
Paulett