1. Get some webspace.
Webspace can be expensive for a decent quality package, but lots of people have been raving about this which was posted on the Dogs On Acid forums a while ago. I haven't signed up myself yet, but it seems a bona-fide offer, and very high quality.
2. Encode your tunes to mp3.
You don't have to use mp3, though it is probably the most widely supported compression standard. I would recommend encoding at AT LEAST 128kbps - probably better to use 256kbps. You will end up with bigger files, but if you've used the above offer then you have oodles of space & bandwidth, so the only other consideration is upload / download speed - and most people are on broadband these days, right?
3. Upload your files to your webspace.
Your webspace provider will give you all the information you need to do this. If you're hardcore then most Operating Systems come with a command-line FTP (File Transfer Protocol) client built-in. However, it's often much easier to use a nice (free) client, which will do handy things like remember settings for different sites etc. I'd recommend CuteFTP or SmartFTP for Windows.
In general, all you will need to use an FTP server is an address, (e.g. upload.mywebspace.com, ftp.mysite.com, or something similar), a port number, (most FTP servers use port 21, but it's possible they may have changed this), and a username / password.
Consult your webspace provider's FAQs etc. for more detailed / specific information.
And that's about it.