If it comes pre-bundled, click link, that opens in Podcasts app, click Subscribe.
If it doesn't, they've still currently got podcast integration with iTunes desktop, which means there will still be an iTunes page and itunes links will work, they just won't redirect to the itms-podcast protocol or whatever it is. They could link to the app from there.
But a much better way would have just been to add a "subscribe" button to podcasts in the itunes store, even if they were still in the music app, (which was once called the "iPod" app). Just as magazines in Newstand are allowed to let users subscribe and download new issues in the background.
Being in the music app also allowed them to be searchable by spotlight, which even gave you a blue indicator of what episode was un-listened.