Crystal,
Uploading audio and video files to WordPress using the Media Uploader is a cinch. Even though the media uploader recognizes these files and display appropriate file-type icons next to them, WordPress does not have a media player that can play these files.
Firstly, you need to install and activate oEmbed HTML5 audio plugin. After activating the plugin, go to the post or page where you want to add audio file.
Click on Add Media button to upload audio file from your computer. You can upload files in mp3, ogg, and wav formats. Once you have uploaded the file, copy file location and paste the raw URL in your post. In other words, DON’T use the Insert Into Post function from the media page. Instead, grab the entire file path and paste all of it (ending in mp3) into your post and it will generate a little player like this:
