Hi Rebecca,
There are a number of ways the scientists are discovering planets around other stars.
One way is to look for a wobble in a star that is due to the gravitational pull of something going around it. To see this you have to look very carefully at the light from the star. The wobble can be detected by looking for changes in color ("Doppler shifts") of dark lines seen in the spectra of a star. The spectra is what you get when you spread light out into different colors, like you do with a prism.
Another way is to look for changes in the amount of light from a star caused by a planet coming between us and the star.
Many planets around other stars have been found at this point. It is very exciting. It used to be that people thought there were probably planets around other stars, but no one could prove it. Now we know for sure they are out there.
Here is a link to an article which is a little old now - more planets have been discovered since it was written, but it gives more information about the how planets are discovered:
http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question10.htmlCheers,
Terry