Did you wait until Pandora went public today to try out its service? If you are new to the gold standard of Internet radio, your first stop should be Donald Bell's video, which covers the basics of Pandora, such as creating a station, giving a thumbs up or a thumbs down to a song, finding lyrics, and buying a song from iTunes or Amazon.
After listening to a given station for a time, you might begin to notice the same songs cycling through the playlist. There are two features that can shake up the song selection, two features that aren't as drastic as giving a thumbs down to a song. (A thumbs down prevents that song from ever playing again on that station.)
The first is the Add variety button. This button resides under the name of the station you are listening to. As the name suggests, it's a way to add variety to your station, beyond the artist or song used to create the station. Adding another artist or song to the station--a "seed," in Pandora's parlance--pulls in songs, according to Pandora's algorithm, that have similar qualities to the artist or song selected. Adding a second seed expands the types of songs you'll hear. That is, Pandora does not try to triangulate songs based on the two criteria. As Pandora explains on its FAQ page:
The various seeds on a multi-seed station do not influence each other in any way. In other words, a station based on a rock artist and a jazz artist will play roughly half rock and half jazz, but the songs you hear won't tend toward a fusion of rock and jazz unless you pick artists known for that style of music.
The other tool you can use is the "I'm tired of this track" button, which you can access from the menu button located between the thumbs up and thumbs down button. As Pandora vaguely describes, it puts a "good song on the shelf for a while." And if you have any skips left, it will skip to the next track. Lastly, telling Pandora you have tired of a song removes it from all of your stations, which might be useful if you have a number of similarly styled station.
One final note: these two features are available on the Web client but not on the mobile version of Pandora. On an iPhone and an iPad, you have only thumbs up and down and skip ability.