It's pretty straightforward. You bid on ads on the user's behalf, and you show them cat pictures - or nothing, user's choice. The ad revenue still goes to the website and the user doesn't have to see ads. Everyone gets what they want and this is really important sites don't have to opt-in.
I've run large internet sites and we'd get email into our webmaster@ address saying we'd be tipped by some users and if we went to sign up we could claim our $3.35 or something. Nobody got time for that. Just use the existing payment rails (the ad system).
If over time the sites saw more people using this, they might change their business model to support subscriptions or something and cut the exchanges out of the middle, but to start, this would work.
I hate how everyone wants to reinvent the wheel. looking at you Brave. We don't need cryptocurrency to solve this.