There are many ways to add music to your blog. The most common way is to embed it into your post, or in New Blogger (formerly Blogger beta), add it as a HTML/Javascript widget via the "Add a Page Element" in the Layout.
You will first have to find a music file that is already hosted on the web, or if you have your own music file stored in your computer, upload it into a file host and then get the URL of the file. If you don't have any music file saved in your computer to upload, you can find files already hosted at
freemp3mail.com, select the artist, click "Free Download" and you will be taken to the file hosted on the web. You can copy the URL from the address bar of that page. For example, this is a file already hosted on the web:
Josh Aran (Blossom).
In the HTML/Javascript widget window or the post editor window, paste this code: