Kimberlee So podcasts run via RSS feeds. Like that's the core protocol.
So the Nerd & Tie website runs a wordpress installation, and then I use the Blubrry Powerpress plugin which adds some podcasting features to it. Some of the shows on the network (the "associated shows" and not the "network owned shows" -- we have a complicated structure) use other stuff, like Bree's Hex Positive uses Spotify for Podcasters (which used to be called Anchor fm) -- but in the end, what gets it into podcatchers is the RSS feed that software produces.
If you look at the Nerd & Tie website you always can find an RSS feed for every show in the subscribe links for people who are using software that supports just directly importing from a feed.
To get listed in places like Apple Podcasts, Spotify, etc all you have to do is sign up, enter the URL for the RSS feed for your show, and then they'll have you verify some stuff (like the email listed on the RSS feed) and bob's your uncle.