How To
You can easily put MP3 files on your website and most surfers will have an MP3 player. If you are worried about bandwidth then you can download RealAudio's free version of Producer and create your own .ra and .ram files - have a look at Zap's Music On The Net Tutorial which also includes the most common mistake when putting music on a Geocities site.
Is It Legal?
The big problem with putting music on a website is the copyright law. Every signed band has their music protected by the Copyright laws through their publishing deal. This applies to any unauthorised live recordings as well.
Non-Commercial Use
What if your website isn't selling anything but just providing music for the entertainment of others? Well, I'm afraid that doesn't qualify you for free music. You need a license to copy and use the work on your even if you won't be charging people to view your site as well as a public display license.
Short Samples
The de minimus rule allows for copying of small amounts of a published work of art without infringing copyright. The problem is that there is no definition over what constitutes a 'qualitatively substantial portion ' of the work in question. Note the use of the word 'qualitative' - rather than quantitative - that is, it's a value judgement rather than a rule which says that 5% is ok. This puts it in the realm of lawyers and they can be very expensive.
Options
You could pay the money to ASCAP, BMI or SESAC for website music licences. These can be on a percentage of website revenue but with fairly substantial minimum payments. You could check existing services such as Launch but all that will give you is the ability to select a type of music to be streamed to listeners. You can sign up for a Live365 radio station but this will cost you around $10 per month and only covers the copyright for music published by the big US publishers above. If you check every track you want to play against their databases then you are covered legally.