There are a few ways to make a transparent background, but like Varelse mentioned, not all are supported in the version of Photoshop you have, and even if Photoshop supports it, not all web browsers support it.
Ideally, if you want "true transparency", you want to use a format that supports a transparent background. 24bit PNG format will work, but on a Windows machine, it won't be supported on the web until IE 7 (and even then, I'm not sure if IE will support it until the next OS comes out). I'm not sure if the current version of Firefox supports it - again, it may be OS-dependent. Illustrator EPS supports transparency, but EPS is a strange format in that you can save that format in Photoshop, but it's not a "true" EPS in the sense that it's still a raster format. "True" EPS should be a vector image. All the may or may not make sense to you, and may be more than you need to know  .
You can simulate transparency in 8bit images, but it takes a good deal of programming to make it work. Basically, you want to change the background to a color that is not used anywhere else in the image. Then, through code, tell the page to ignore the RGB values. However, 8bit images are usually not overly pretty.
The easiest (and probably the best) way to do this, with the version of PS that you have, is to save the image for web, select a GIF format, and select the Transparent check box.
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