I'm sure somebody else knows a lot more than I do, but this document might get you started: http://www.tldp.org/HOWTO/MP3-HOWTO.html
Basically (as I understand it anyway), to do more than just send the file via HTTP and have the listener listen as it downloads, you need software running on the server to stream it (like Icecast, for example). I don't remember DreamHost having any of these installed, and since they would need a port on a shared server, I'm doubting that you'll be able to. If you had a dedicated server, that'd be different, of course, and I could be entirely wrong.
Your other option would be streaming QuickTime audio; if you're on any plan other than the basic L1 version, you've got access to QuickTime streaming, which in my experience works quite well. You even have the option of just packaging the quicktime file as a stream-ready file (can't remember the settings right now) and embedding it in a page, at which point it will download via HTTP and play live as soon as it's buffered a bit--no special set up required.
Of course, QT streaming is going to require you use qdesign music or Qualcomm PureVoice for compression, and your users are going to need Quicktime installed (not that big a deal if you ask me). Not quite as "cool" as MP3 streaming, and not as flexible for the end user, but not bad.
Although you can't package an MP3 as a QuickTime file for streaming (as far as I know, anyway, though I could be wrong), you can use MP4 audio, which has very nice quality and is included in QT6 (preview only, currently, but at least its available free now for Mac and Win platforms). MP4 is more than likely going to be a common standard format, so in a while those files might be as end-user flexible as MP3s (though the MPEG consortium is trying hard to hold it so tight it strangles).
Anyway, I hope that helps a bit, but one more word of caution: if you've got plenty of money for bandwidth or aren't expecting a lot of listeners, no problem, but if you're on a tight budget, be careful. 50 people listening to 5 minutes of 128kbps music per day adds up to 7 or so GB of data transfer; get really popular, and things could get expensive quickly.