Audio posts require the use of the Adobe Flash player, though very common place on most browsers today, it is typically an external add-on.  Get the Flash Player from Adobe, Inc to enable this functionality and listen to the Audio posts on-demand.  Of course you can always download the file and listen on your favorite media player, but the on-demand listenening functionality should let you preview the audio before you download.

This answer is a bit tricky if you are new to listening to internet radio.  So here are some guidelines by Operating System:

Linux (Fedora, Debian, Ubuntu, etc)

All the live shows can be accessed from the same everyday streams that are provided at The Vinyl Project.  Simply tune in to the stream (Ogg or MP3) that you prefer at the scheduled showtime.  The rotating radio streams will be automatically cut-over to the live shows when they start.  Pay attention to the timezone listed on the shows' schedules.  Most shows will be in EST (Eastern Standard Time).