I know it's a stupid detail, but I'm pretty sure the font in the first minute used to spell "Nicolaus Coperinicus" is the Liberation Serif, the default font for the LibreOffice software. Cool.
You'll first need a podcatcher. If you're on iOS, a really basic podcatcher is made by Apple: just search for the "podcasts" app on the App Store. If you're on Android, you'll have to find an option from someone else (some guides I found online suggest Google Play Music has podcasting functionality built in, but I tried it myself and it didn't have it), Stitcher is supposed to be a good app for beginners. Stitcher also seems to have an iOS app, if you'd prefer that. I personally use Pocket Casts, which I would highly recommend, but it does have small one-time cost associated with it, so it's probably not the best choice for someone unsure if they'll like podcasts.
From there, whichever app you go with, it should have a search option. Search for the podcast you want, hit subscribe, and start downloading episodes to listen.