Podcasts went mainstream in 2014. We can thank Serial for that. But even as podcasts take off in popularity, I sense confusion from people as to how they should manage their podcasts.
Firstly, iTunes is not your only option. It's a fine option, particularly for the desktop / laptop, but there are many excellent alternatives.
I have an Android phone. I've noticed several very good podcast apps that only cost a few dollars, but there's also an excellent free app I've been using lately. It's called Podcast Addict and you can download it from Google Play here.
Once Podcast Addict is installed on your Android device, simply click the + button at the top to add a new podcast. You're presented with several options for adding a new podcast, as shown below.
You could add the RSS feed for my podcast, which is https://www.torontomike.com/torontomiked.xml, but it's probably easier to search for "Toronto Mike'd".
It's that simple. You're now subscribed to Toronto Mike'd (or any other podcast you're interesting in) and it's easy to manage which episodes you download and listen to.