If you purchased the Don't Starve Soundtrack from Steam, it gets downloaded to the Don't Starve game folder within your Steam folders. There are two ways to access your music via Steam:
1) Via Steam Music Player
On your Steam client, click on "View" on the upper left-hand side and choose "Music Player." From there, you should be able to listen to all of the music on your PC. Please note that you'll have to point Steam to the MP3s on your computer, then browse your collection of albums and artists.
More info on Steam Music Player here: http://store.steampowered.com/news/14358/
2) Via your local Don't Starve files + Local Audio player
The other way to get your soundtrack folder is by right-clicking on Don't Starve in your Steam game library and choosing "Properties." In properties, click on the "Local Files" tab and choose "Browse Local Files". This will open up your Don't Starve folder in Steam where you'll find the folder for your soundtrack.
From there, just run the soundtrack with your preferred audio player, or load it up onto your audio device for listening on the go!