The web-player on the homepage, or the 'm3u' or 'Direct' links above should get some music playing in your phone or computer's browser.
If that doesn't work or if you would like more control and to see the track names (when available), try playing the audio stream in your faviourite audio player app. Most have a "connect to internet broadcast/stream" option. If you don't have an audio player, you can try VLC from the 'VideoLAN' project. You can get the app on Android and iPhone too (make sure it's from VideoLAN). It may not be the smoothest and coolest player around, but it is totally and completely free. No ads, no trial periods, no nothing.
To play the stream in your audio player app, you'll need to copy-paste the stream URL into the player by right-clicking or long-pressing on either the 'm3u' or 'Direct' links above to copy the link location. In VLC on iOS, it's Network->Open Network Stream. In VLC on Android go to Stream in the main menu.
Also, very important... connect your device to some decent speakers and enjoy!