There's no need to embed any code on anyone's site. The whole point is that Readability automatically detects the main body content from a page and extracts it.

As a publisher, if your main body content isn't being detected automatically, probably because your HTML is awful, you can add some classes to the key elements to fix that. But that's not necessary.

There's also no need to register as a publisher to receive contributions. From their FAQ:

"Readability keeps track of pages visited even before a publisher registers with us to view their statistics. If your site has garnered traffic to Readability, we’re already earmarking money for you."

https://www.readability.com/faq/#view-plainGuidelines

However, you will need to register to actually get the funds.