The default mechanism for inserting a player in a post is to use the [audio] syntax:
This will insert a player and load your_mp3_file.mp3 into it.
Using the WordPress Media Library
This is by far the simplest way of using Audio Player. If you are using WP 2.5 or higher, you can use the Add Audio button:
After select a file from your computer and uploading it via the Media Library screen, select the Audio Player option for the Link URL:
click Insert into Post and the correct audio code will be inserted.
Setting a default location for your audio files
You can configure Audio Player with a default audio files location so you don’t have to specify the full URL everytime. You can set this location via the Settings panel (at the bottom of the General tab). Once set, you can use this syntax:
Audio Player will automatically look for the file in your default audio files location. This can be very handy if you decide to move all your audio files to a different location in the future.
About enclosures (This is important)
An enclosure is similar to an email attachment for a blog post. Enclosures are the basic mechanism for podcasting. When a post contains a link to an audio file, WordPress automatically sets up an enclosure for that post. This means that people who are subscribed to your blog feed will be presented with a link to the audio file (your feed is now effectively a podcast).
This is good if you are OK with people downloading the file. If you are not, then you really shouldn’t use Audio Player. For now, the only way to prevent this is to manually remove the enclosure everytime you publish or save the post. Open the Custom fields section of the post screen to see and remove enclosures.