Depends on your platform. There's a desktop program called Juice that lets you add the RSS feeds to download your shows. On Android there is an app called Antenna Pod. Both are free and open source if that matters to you. I used to use Juice and from what I can tell now it's no longer updated but it probably still works and probably has forks that work just fine. I also used to use an app called Pocket Casts. But I haven't used it in years and last I read it got sold to some communists who made it free. And edging further into sketchy territory, could also use Spotify which has been gobbling up podcasts and holding them in their walled garden.
Just using youtube-dl to download them isn't a bad idea in theory but I'd imagine it would get complicated soon if you follow a lot of podcasts and listen to a lot of episodes. And podcasts used to just be RSS feeds that would get updated with descriptions to episodes that you could download so it used to not matter which program you used or if you just downloaded shows directly. But again Spotify is buying up some podcasts so if shows you want have gotten pulled into that eco system you might have to use that program.
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