Podcasts should play on most computers without any effort, although your particular browser and options may affect your experience. If you are using a fully-current browser, you should not need any plug-ins or add-ons enabled, whether on a full computer, tablet, or mobile phone. Some features, such as recent podcasts, lecture progress, short-jumps, and modified playback speed require Javascript. A video player with a reduced set of options should automatically load without javascript.
In all cases, you can right-click Download to download the file to your computer, where you can play it in any media player.