Add it to my "backlog" folder that I have a program that picks from whenever there's under 4 hours of playtime of my playlist. Once I'm through the old episodes I move it to the regular folder of podcasts that I subscribe to. I abuse Pocket Casts' internal webapp API for this.
(If it is current affairs, I'll subscribe while working on the backlog, so I both listen to the old episodes in order and get new episodes in the playlist).
It depends on the podcast. With MBMBAM I started at the most recent. With Dungeons and Daddies I went to S1E1. With Hey Riddle Riddle I started with the crossover special. With Behind the Bastards I picked whichever subject interested me most in the moment. With We Hate Movies I picked one I'd seen.
Depends on the type of podcast. If its a serialized narrative it's better to start at the beginning. If not, I'll listen to the latest episode and pick whatever I'm interested in from the older ones.
I personally would start oldest to newest just because they might reference something from an older show and so starting at the beginning, just helps give you context for stuff later on.
But I guess it also kind of depends on the podcast too. I listen to a news podcast and some days I just don’t feel like listening to it and so I just skip it. But that’s only because they might be covering a topic. I’m not interested in listening about.
I don't really listen to podcasts often, but when I do they're usually radio play, types. So I'll absolutely start at the beginning.
For others that have topics that are done in pieces, like for Last Podcast on the Left, I'll just usually scroll until I find something that sounds interesting. I absolutely love their Black Plague episodes, or The Donner Party ones.
I used to be a completist and would start at ep 1. Now, if there is a big back catalog I'm more likely not to listen to the podcast at all and will only rarely get in at the current episode.