To see these working on my chess blog, go here.
Obviously this is a very simple player! But it works and though it may not be obvious, you can drag to raise and lower the volume and you can scrub back and forth within the song.
1) Save your audio as an mp3 file, which you can do in a variety of programs.
2) You will need to upload the file to a server on the web so you'll have a URL to point to. I use FileDen, which has a lot of annoying ads but is free. Just go to FileDen.com, sign up, and then upload.
3) Once the file is uploaded, you will see its URL at the bottom of the window, as in this image:
4) Copy the URL to the clipboard.
5) In WordPress, in your "New Post" window, go into html mode.
6) Enter the following code but substitute your URL for mine, although of course you could test it with mine. Yes, it's just the word audio followed by the URL, with the whole thing inside of brackets. Simple enough!
[audio http://www.fileden.com/files/2009/3/31/2386669//Musicals - A Chorus Line - Sing.mp3]
7) Publish and play.
Second Player (SoundCloud)
1) Go to soundcloud.com and join (for free).
2) Record, upload or search for music.
3) When you have your track, click on SHARE then WORDPRESS then copy the EMBED short code
4) In WordPress new post window, go into html mode, then paste in the code.
5) Publish and play.
For more info: http://en.support.wordpress.com/audio/