instructions given on spotify site to try out the Spotify for Linux work-in-progress.
Debian
# 1. Add this line to your list of repositories by
# editing your /etc/apt/sources.list
deb http://repository.spotify.com stable non-free
# 2. If you want to verify the downloaded packages,
# you will need to add our public key
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 94558F59
# 3. Run apt-get update
sudo apt-get update
# 4. Install spotify!
sudo apt-get install spotify-client
# that is all.