There's currently no way to embed a whole Podpage site inside another website. Your Podpage is a complete website with many pages and sections, so it can't be dropped into a single page like www.yourdomain.com/podcast.
The closest option — and how most podcasters handle this — is to put your Podpage on a subdomain of your existing domain, like podcast.yourdomain.com. Your main site stays at www.yourdomain.com, your Podpage lives at the subdomain, and you link between the two from each site's navigation.
To set this up, see How do I connect my domain name to my Podpage? — and if you're weighing your options, Should I use a subdomain or a new domain for my podcast?