There are no tricks to using this site - it has been tested on Mac and Windows computers and on iOS and Android portable devices. Let me know if you encounter problems.
You just find the song you want in the left-hand column and click on the corresponding voice part. A window will appear with a control bar that, among other things, allows you to start and stop the music.
The display will be pretty tiny on the smaller phones but you should be able to expand (unpinch) it enough to get to the Pause and Play icons.