A podcast is just an audio file - usually a .mp3 file. The great thing about podcasts is that you don't have to download every individual audio file, you can subscribe - and by doing so your "podcatching" software downloads you subscription onto your machine. Of course you can download each mp3 file separately if you like - but this can be time consuming.
Android Ecosystem: Spotify, or Pocketcast - Pocketcast is a onetime cost - but the upside is the developers which are recognised worldwide are South Australian.
Apple Ecosystem: itunes, but if your OS is XP I recommend Juice, if your OS is Vista or 7 I recommend Hermes, all free. See the video tutorials at the bottom of this page on how to install and use Juice and Hermes - pretty straight forward. To find a podcast "feed" look for either the letters RSS or the symbol.
60 Second Mind from Scientific American. Bite size clips that bring you contemporary information about psychology, particularly recent research.
60 Second Mind feed URL: http://rss.sciam.com/sciam/60-second-mind
All in the Mind 30 minute program from the BBC. All in the Mind feed URL: http://downloads.bbc.co.uk/podcasts/radio4/medmatters/rss.xml
Brain Science Podcast feed URL: http://feeds.feedburner.com/brainsciencepodcast