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.
When there are two parts on one voice (e.g., Alto I & Alto II) the higher part is directed to the left speaker or earphone and the lower part to the right. This separation works best with headphones or earbuds - but you could also adjust the balance on your computer's speakers to emphasize one part over the other.
Please let me know of any errors that you discover.