The artist can contact their distributor or label and ask their music to be uploaded on Spotify.
It's possible for Spotify to get in contact with the label too, but the process is a lot faster artist-side.
Check out this thread for more information. :)
If you're interested in how artists get their music on Spotify, then this website has some interesting FAQ. It's generally meant for artists wanting to get on Spotify, but it's an interesting read for others too.
Hope this clears things up a bit more :)