STEPS
TOOLS
Tap on iTunes
At the bottom tap on more
Tap on podcasts
Here you can pick the podcast of your choice. If there is a specific podcast you want tap on the search at the bottom and type in the podcast you are looking for
Once you get here you have two options tap on the name to stream the podcast or press on free to download the podcast to for later listening. Enjoy
 iPhone iPad iPod touch

How to download and listen to your podcasts on iphone

This tutorial is good for any iOS device