There are many ways to listen to podcasts. Each have their pros and cons and may not suit everybody.
In my experience, by far the easiest way to listen is through iTunes . For apple users, the apple podcast app will let you find the show on iTunes and can be set to download each episode automatically. Similarly, subscribing to Legacy breakfast on iTunes will automatically download new episodes for you to listen to.
You can also stream the episode, by either using the audio player in a browser, or again through something like Apple TV.
For non iOS users, the show is also available on stitcher radio here:
For android users, try IP Podcast Player, which lets you subscribe to iTunes podcasts: https://play.google.com/store/apps/details?id=com.itunestoppodcastplayer.app&hl=en_GB
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