Google being Google, the company will try to push you towards its product when you search for a podcast title -- behavior that led to the BBC removing its shows from Google Podcasts. On desktop, Googling the name of your chosen podcast will bring up a list of recent episodes, and clicking one of those will take you to podcasts.google.com to listen.
Annoyingly, going directly to podcasts.google.com doesn't give you the app -- it just directs you to download the smartphone product. To get to the play interface, you have to choose an episode of a particular podcast in search.
However, it's handy that if you're signed in to Google, your account remembers where you got up to in the podcast and syncs it across your devices, so you can continue where you left off.
Google Podcasts' Head of Product Zack Reneau-Wedeen demonstrated the new functionality on Twitter, pitching it as a way to make audio a "first-class citizen" across the company's portfolio:
Google also announced at I/O 2019 that search results will soon show podcast episodes relevant to what you've searched for. So if you look for a particular unsolved crime, for instance, you might get an episode of a podcast dedicated to it under the heading 'Podcasts about this story.'