While the WordPress Support forums at http://wordpress.org/support/
would be the best place to ask this I can point you in the right direction.
First off, on you on WordPress.com? If so, none of my suggestions will be applicable. The below is for a WordPress self hosted blog (WordPress.org)
First look at the Codex for Podcasting, even if you just want to play the file on your site this has a ton of useful info:http://codex.wordpress.org/Podcasting
There are two plugins I have used: PowerPress: http://wordpress.org/extend/plugins/powerpress/
and Audio Player: http://wordpress.org/extend/plugins/audio-player/
If all you want to do is play the mp3 through your site, Audio player is for you. If you want more (mp3 in feeds, podcasting etc) PowerPress is much more "powerful", but it can be harder to configure.