Step 1: First, upload the music file to any free file hosting servers on the net. Once you upload, they will provide you with a direct link to that music file.
http://sample-server.com/uploads/from-the-moon.mp3
Step 2: Here is the code you need to add music to your blog
<embed width="250" height="50" autostart="false" src="MUSIC FILE URL"/></embed>
Step 3: You can add the music player anywhere you want in your Blogger blog..
Sidebar: If you want to add in sidebar, go to Design --> Add a gadget --> HTML / JavaScript --> and paste the code and save it.
Blog Post: If you want to embed music file to any specific blog post, Paste the code in 'Edit html' mode and save it.
Step 4: Done / Enjoy
clarification code above:
width: width of the music player
height: height of the music player
autostart: values : false or true
MUSIC FILE URL: the direct link to your music file
In this example, MUSIC FILE URL is http://sample-server.com/uploads/from-the-moon.mp3