The podcast creators themselves insert them in by speaking them. Which, now that I think about it, is bullshit, since I pay $10/month or whatever for "ad-free Spotify."
Right now you can listen to podcasts that are years old and yet the ads that play are current. This means they've been recut with new ads, probably automatically.
I notice this most on the Ezra Klein podcast. I don't think it's Spotify that's helping this podcast achieve this functionality, but in future Spotify will certainly be providing this ability to podcast producers, if it isn't already.
I'd expect that in the near future the podcasts you listen to will be dynamically stitched together so that I hear ads tailored to me, which are different from the ads you hear. Different users will also get different ads loading.