The good news is that iPhones and iPods are the perfect devices for listening to podcasts. In fact, the "pod" in "podcast" actually comes from the iPod device name, if you didn't know that already! The bad news, though? As far as I can tell, you can't delete podcasts or any other content from your iPod or iPhone directly. You need to instead use iTunes on your computer, then resync your iOS device.

Therefore, to get started, you need to launch iTunes on your computer.

Then, look on the left. You'll see this:

Here you can see that I clicked on "Podcasts" and it showed me icons for each of the podcasts I have on subscription, namely Boulder Open Podcast [iTunes link], a podcast that I co-host, as it happens!

Click on the podcast icon and you'll see considerably more detail, including episode names, etc:

All done with this podcast? Click on "Unsubscribe" on the lower left. Instead, though, you might well want to consider just changing your subscription preferences so that the very latest episode or two are save and all the older episodes are automatically deleted to save space. You can do that by clicking on "Settings..."

Click on the checkbox next to "Use Default Settings" and you can tweak the settings:

As you can see, there are lots of ways to customize the settings on a per-subscription basis, which is really useful.

When you have everything set the way you want, plug in your iPod / iPhone and sync it. Done!