Valve have been building out their Steam Operating System or SteamOS since the beta's launch and the next feature coming to the OS will allow users to play back local music files via the SteamOS overlay.
In order to request access to the Steam Music beta, all you need to do is join the Steam Music community group here. Then, hope to be randomly selected as Valve will be inviting waves of beta testers into the program over the coming weeks. Eventually all Steam users will have access to the new SteamOS music playback.
Obviously, this addition doesn't mean much to computer users who can launch Winamp or iTunes or whatever they like to listen to music with while they're playing games on their desktop computer. This new feature is more geared toward those users experimenting with Big Picture Mode and possibly their very own Steam Machine beta box.
If you've built your own or plan on getting a Steam Machine this year, you should definitely join the Steam Music group now. Valve unveiled the hardware and SteamOS initiatives last year, with every Steam Machine hardware partner showing their goods at CES this year. Valve sent out their own beta Steam Machine boxes to lucky fans too. You can check out the company's specs here.