With no surprise, Google has announced they are moving away from the first click free program, which is how Google handled paywalled content in search for a decade with what they are calling “flexible sampling.”
Flexible sampling is offered in two formats, either metering or lead-in formats. Metering provides users with a quota of free articles to consume, after which paywalls will start appearing. Lead-in offers a portion of an article’s content without it being shown in full.
This FCF and now flexible sampling is all about making sure spammers don’t use cloaking techniques. So to help with this, Google is asking publishers who use these methods to also markup their content with new structured data for paywalled content. The documentation is pretty clear and how it works, and it seems pretty simple to use, so look into it. Although, it seems not to work yet with the Structured data testing tool:

Hey @googlewmc @JohnMu the cssSelector you recommend for #paywall #jsonld is not recognized in the testing tool. https://t.co/fEQu20j92O pic.twitter.com/2athLbGAbU
— Tobias Willmann (@WillmannTobias) October 2, 2017
John Mueller from Google replied:

Yes, it’s new :). I’ll double-check, but I think it’s just a matter of time until that’s updated too. Thanks for nudging!
— John ☆.o(≧▽≦)o.☆ (@JohnMu) October 2, 2017
Greg Sterling wrote up some more of the backstory on this for the business reasons.
Here is what Google wrote about metered content:

In general, we think that monthly, rather than daily metering provides more flexibility and a safer environment for testing. The user impact of changing from one integer value to the next is less significant at, say, 10 monthly samples than at 3 daily samples. Monthly metering also has the advantage of focusing paywall hits on your most engaged users, who are those most likely to subscribe, while allowing your newer and less engaged users to become acquainted with the value of your content before experiencing a paywall. (“Paywall,” in this context, applies equally to barriers that require either subscription or merely registration for content access.)

Here is what Google wrote about lead-in content:

Some publishers show the first few sentences of an article “above the fold” of their paywall. We think this is a good practice. By exposing the article lede, publishers can let users experience the value of the content and so provide more value to the user than a page with completely blocked content. Lead-in also generates user curiosity about how article continues, which may assist in conversion.

Forum discussion at Twitter.