Adam Vine Sorry for the late response. It's been a while since I messed with this. It does work though :)
You start by cloning or downloading the .zip from github. Inside the unpacked neeo-spotify-master directory, you run 'npm up' to download all the prerequisites via npm. After that, 'npm start' should work.
It should print a URL to the internal web interface, with instructions for the Spotify API setup.
If you're still in trouble, let me know and I'll see if I can't fix it :)