Well that's easy,
http://www.webdesignbooth.com/10-easy-to-implement-flash-based-mp3-players-for-your-website/
A server side script can be used to shuffle the playlist so visitors hear something different every time they visit as an optional feature.
I should point out however that doing this will use a much of your monthly bandwidth allowance very quickly if lots of friends decide to listen regulary*. Streaming the audio uses less data however you do require full control of the web server as software has to be installed as opposed to code uploaded, that means either paying for a VPS (virtual private server) or using your home PC & internet connection.
*
Assuming an average MP3 playing time of 3 minutes and a filesize of 4megabytes..
that's 20 tracks per hour times 4mb 20x4=80
so we have 80 megabytes of site bandwidth
per listener
per hour
Therefore 20 listeners spending an hour on your site equals 20x80 megabytes of bandwidth or 1.6 Gigabytes of data an hour! Don't get me wrong there are some great hosting deals out there but few.. even those offering 'unlimited' monthly traffic would put up with this kind of load for long.