My suggested and recommended way of listening to this podcast - and any other podcast that you want to listen to on a regular basis - is to subscribe to the podcast feed. This will usually involve the use of a podcatcher, such as iTunes, Juice, WinAMP, gPodder, BeyondPod, etc. In order to use these, you'll need to refer to the help section of one of these applications.
To subscribe to The Bugcast, simply paste the feed URL into your chosen podcatcher:
http://www.thebugcast.org/feed.xml
Alternatively, if you're using iTunes, use the following link to the iTunes Music Store:
The Bugcast on the iTunes Music Store
If subscription is not an option, you can always listen from the website itself. The main show page at:
http://www.thebugcast.org/shows/
... will always show the most recently published episode. You can click on the "Listen now" link on the right-hand side to listen to any show. You can also use the back and forward links, just below the navigation bar, to jump between episodes.
Most episodes of The Bugcast are broadcast live on Fridays at 21:00 UK time (what time is that in my timezone?).
You can join in by visiting The Bugcast Chatroom by clicking on the Chatroom/Listen Live link above, or by clicking on this link:
http://www.thebugcast.org/live
... or you can go straight to IRC on the Freenode network, and /join #thebugcast
... and interact with the others who are listening live!