If you are a beginner dancer, listening to swing music will help your dancing immensely! If you don't have a swing music collection of your own, there are several places to hear the music online for free! You may be prompted to download a browser plug-in or a helper application if you don't have it, although most newer PCs come with the more common ones pre-installed. The music players all have free versions, which are good enough for listening to web radio. Note that web radio works best with a broadband connection. You can listen with a dial-up connection, but the music may cut out frequently.
To get you started, here are a few. This is just a small sampling, you can find many more by searching!