The standard way to do this is a catch-and-release portal which requires agreement with terms and conditions, and could contain advertisements - including paid links to relevant content. Plenty off-the-shelf software offers this. You could go as far as to extend this to require a password to log in - with the password being the answer to something in a video on the site which would need to be watched to acquire it.
It is technically possible to intercept http traffic and modify it on the fly to include paid content but depending on jurisdiction this could be against the law (as it's a form of MITM attack). You will also struggle to monetise https sites as it will trigger warnings in browsers.
1This is known as a captive portal. – jcbermu – 2017-12-26T09:25:50.113
...also known as a 'not going to touch this with a barge-pole' portal ;) – Tetsujin – 2017-12-26T10:30:02.517