If you purchased the Don't Starve Soundtrack from Steam, you will be able to install and listen to it via Steam, or move it to your other music players.
Go to your Steam Library and on the dropdown box just below the search bar on the left hand side, click on the dropdown arrow and change from GAMES/ALL to SOUNDTRACKS. This will list all of the soundtracks you own on your Steam account. Right-click on Don't Starve Soundtrack in your Steam game library and choose "Download Album."
Once installed, click on Don't Starve Soundtrack and all of the songs installed will be listed on the song list to the right of your library screen.
OR, you can right-click on Don't Starve in your Steam game library, choose "Properties", click on the "Installed Files" tab and choose "Browse...". 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 you can load the song files onto your audio device for listening on the go!