Arch Linux Spotify
You can install Spotify on Arch Linux like this:
sudo pacman -S spotify
This will install the Linux client that is produced by Spotify. It is not actively supported as it is apparently developed by Spotify engineers in their spare time.
You can also just use the web player from a browser which should work fine. There are also a number of third party clients that should work great. These include Clementine. You can find a list of these clients and more details/tips for Spotify on Arch here: