The only way to upload an MP3 music track to Facebook is by using a third-party app. The site used to have a built-in music player app, but it was discontinued in late 2010. Some of the third-party apps that allow a Facebook user to upload MP3s include RootMusic, ReverbNation, Bandcamp and Audioboo.
If one decides to upload a track using Audioboo, the user needs to open the Audioboo app via Facebook, select the new file upload function, click on Select a File and choose the MP3 he wishes to upload. Then, he needs to title the track and click Publish. Once the track has uploaded, he simply needs to copy the URL associated with it. If he pastes that URL onto his Facebook page in the Status Update box, the track should appear.
In lieu of uploading an MP3, a user can share audio tracks by sharing a video of the song in question. To share a personal video, the user hits the Add Photos/Video button, which is to the right of the Update Status button. Then, he hits Upload Photos/Videos. This opens a File Upload window, and the user simply needs to click on the desired video. If he wants to share the video of a song from YouTube or any other video sharing site, he simply needs to copy the URL to that video and paste it into the Status Update box.