Sorry if I'm wrong, but you might be confused.
Spotify works from the client that you download on your computer:
Spotify also works on mobile devices if you have a Spotify premium subscription.
The Spotify website is for reference and support.
Rdio, which is a similar service like Spotify has music streaming available through their website.
Spotify's experience is different and works through a program that gets installed on your computer or mobile device.
If you are on your computer, try to look around for a program called Spotify.
If you don't have it on your computer you can download it from here: